What rate of interest compounded annually is required to triple an investment in 8 years?
What Is Compound Interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods. Show
"Interest on interest," or the power of compound interest, is believed to have originated in 17thcentury Italy. It will make a sum grow faster than simple interest, which is calculated only on the principal amount. Compounding multiplies money at an accelerated rate and the greater the number of compounding periods, the greater the compound interest will be. Key Takeaways
Understanding Compound InterestHow Compound Interest WorksCompound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value. Katie Kerpel {Copyright} Investopedia, 2019.The formula for calculating the amount of compound interest is as follows:
= [P (1 + i)n] – P = P [(1 + i)n – 1] Where: P = principal i = nominal annual interest rate in percentage terms n = number of compounding periods Take a threeyear loan of $10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be: $10,000 [(1 + 0.05)3 – 1] = $10,000 [1.157625 – 1] = $1,576.25 The Power of Compound InterestBecause compound interest includes interest accumulated in previous periods, it grows at an everaccelerating rate. In the example above, though the total interest payable over the three years of this loan is $1,576.25, the interest amount is not the same for all three years, as it would be with simple interest. The interest payable at the end of each year is shown in the table below. Compound interest can significantly boost investment returns over the long term. While a $100,000 deposit that receives 5% simple annual interest would earn $50,000 in total interest over 10 years, the annual compound interest of 5% on $10,000 would amount to $62,889.46 over the same period. If the compounding period were instead paid monthly over the same 10year period at 5% compound interest, the total interest would instead grow to $64,700.95. Compound Interest SchedulesInterest can be compounded on any given frequency schedule, from daily to annually. There are standard compounding frequency schedules that are usually applied to financial instruments. The commonly used compounding schedule for savings accounts at banks is daily. For a certificate of deposit (CD), typical compounding frequency schedules are daily, monthly, or semiannually; for money market accounts, it’s often daily. For home mortgage loans, home equity loans, personal business loans, or credit card accounts, the most commonly applied compounding schedule is monthly. There can also be variations in the time frame in which the accrued interest is credited to the existing balance. Interest on an account may be compounded daily but only credited monthly. It is only when the interest is credited, or added to the existing balance, that it begins to earn additional interest in the account. Some banks also offer something called continuously compounding interest, which adds interest to the principal at every possible instant. For practical purposes, it doesn’t accrue that much more than daily compounding interest unless you want to put money in and take it out on the same day. More frequent compounding of interest is beneficial to the investor or creditor. For a borrower, the opposite is true. Compounding PeriodsWhen calculating compound interest, the number of compounding periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest. The following table demonstrates the difference that the number of compounding periods can make for a $10,000 loan with an annual 10% interest rate over a 10year period. Compound Interest: Start Saving EarlyYoung people often neglect to save for retirement. For people in their 20s, the future seems so far ahead that other expenses feel more urgent. Yet these are the years when compound interest is a gamechanger: Saving small amounts can pay off massively down the road—far more than saving higher amounts later on in life. Here's one example of its effect. Let’s say you start investing in the market at $100 a month while still in your 20s. Then let’s posit that you average a positive return of 1% a month (12% annually), compounded monthly across 40 years. Now let’s imagine that your twin, who is the same age, doesn’t begin investing until 30 years later. Your tardy sibling invests $1,000 a month for 10 years, averaging the same positive return. When you hit your 40year savings mark—and your twin has saved for 10 years—your twin will have generated about $230,000 in savings, while you will have a bit more than $1.17 million. Even though your twin was investing 10 times as much as you (and even more toward the end), the miracle of compound interest makes your portfolio significantly bigger, here by a factor of a little more than five. The same logic applies to opening an individual retirement account (IRA) and/or taking advantage of an
employersponsored retirement account, such as a 401(k) or
403(b) plan. Start it in your 20s and be consistent with your payments into it. You’ll be glad you did. Pros and Cons of CompoundingThough the miracle of compounding has led to the apocryphal story of Albert Einstein calling it the eighth wonder of the world or man’s greatest invention, compounding can also work against consumers who have loans that carry very highinterest rates, such as credit card debt. A credit card balance of $20,000 carried at an interest rate of 20% compounded monthly would result in a total compound interest of $4,388 over one year or about $365 per month. On the positive side, compounding can work to your advantage when it comes to your investments and be a potent factor in wealth creation. Exponential growth from compounding interest is also important in mitigating wealtheroding factors, such as increases in the cost of living, inflation, and reduced purchasing power. Mutual funds offer one of the easiest ways for investors to reap the benefits of compound interest. Opting to reinvest dividends derived from the mutual fund results in purchasing more shares of the fund. More compound interest accumulates over time and the cycle of purchasing more shares will continue to help the investment in the fund grow in value. Consider a mutual fund investment opened with an initial $5,000 and an annual addition of $2,400. With an average annual return of 12% over 30 years, the future value of the fund is $798,500. Compound interest is the difference between the cash contributed to the investment and the actual future value of the investment. In this case, by contributing $77,000, or a cumulative contribution of just $200 per month, over 30 years, compound interest is $721,500 of the future balance. Of course, earnings from compound interest are taxable, unless the money is in a taxsheltered account. It’s ordinarily taxed at the standard rate associated with your tax bracket and if the investments in the portfolio lose value, your balance can drop. Compound Interest InvestmentsAn investor who opts for a dividend reinvestment plan (DRIP) within a brokerage account is essentially using the power of compounding in whatever they invest. Investors can also experience compounding interest with the purchase of a zerocoupon bond. Traditional bond issues provide investors with periodic interest payments based on the original terms of the bond issue and because these are paid out to the investor in the form of a check, the interest does not compound. Zerocoupon bonds do not send interest checks to investors. Instead, this type of bond is purchased at a discount to its original value and grows over time. Zerocouponbond issuers use the power of compounding to increase the value of the bond so it reaches its full price at maturity. Compounding can also work for you when making loan repayments. Making half your mortgage payment twice a month, for example, rather than making the full payment once a month, will end up cutting down your amortization period and saving you a substantial amount of interest. Tools for Calculating Compound InterestIf it’s been a while since your math class days, fear not: There are handy tools for figuring out compounding. Many calculators (both handheld and computerbased) have exponent functions you can utilize for these purposes. Calculating Compound Interest in ExcelIf more complicated compounding tasks arise, you can perform them in Microsoft Excel in three different ways:
Other Compound Interest CalculatorsSeveral free compound interest calculators are offered online, and many handheld calculators can carry out these tasks as well:
How Can I Tell if Interest Is Compounded?The Truth in Lending Act (TILA) requires that lenders disclose loan terms to potential borrowers, including the total dollar amount of interest to be repaid over the life of the loan and whether interest accrues simply or is compounded. Another method is to compare a loan’s interest rate to its
annual percentage rate (APR), which the TILA also requires lenders to disclose. The APR converts the finance charges of your loan, which include all interest and fees, to a simple interest rate. A substantial difference between the interest rate and APR means one or both of two scenarios: Your loan uses
compound interest, or it includes hefty loan fees in addition to interest. Even when it comes to the same type of loan, the APR range can vary wildly among lenders depending on the financial institution’s fees and other costs. You’ll note that the interest rate you are charged also depends on your credit. Loans offered to those with excellent credit carry significantly lower interest rates than those charged to borrowers with poor credit. What Is a Simple Definition of Compound Interest?Compound interest simply means that the
interest associated with a bank account, loan, or investment increases exponentially—rather than linearly—over time. The key word here is compound. Suppose you make a $100 investment in a business that pays you a 10% dividend every year. You have the choice of either pocketing those dividend payments like cash or reinvesting them into additional shares. If you choose the second option, reinvesting the dividends and compounding them together with your initial $100 investment, then the returns you generate will start to grow over time. Who Benefits From Compound Interest?Compound interest benefits investors, but the meaning of investors can be quite broad. Banks, for instance, benefit from compound interest when they lend money and reinvest the interest they receive into giving out additional loans. Depositors also benefit from compound interest when they receive interest on their bank accounts, bonds, or other
investments. It is important to note that although the term compound interest includes the word interest, the concept applies beyond situations for which the word is typically used, such as bank accounts and loans. Can Compound Interest Make You Rich?Yes. Compound interest is arguably the most powerful force for generating wealth ever conceived. There are records of merchants, lenders, and various businesspeople using
compound interest to become rich for literally thousands of years. In the ancient city of Babylon, for example, clay tablets were used more than 4,000 years ago to instruct students on the mathematics of compound interest. In modern times, Warren Buffett became one of the richest people in the world through a business strategy that involved diligently and patiently compounding his investment returns over long periods. It is likely that, in one form or another, people will be using compound interest to generate wealth for the foreseeable future. The Bottom LineThe longterm effect of compound interest on savings and investments is indeed miraculous. Because it grows your money much faster than simple interest, it is a central factor in increasing wealth. It also mitigates a rising cost of living caused by inflation, as it will almost certainly outpace it. For young people especially, compound interest is a godsend, as they have the most time ahead of them in which to save. Remember when choosing your investments that the number of compounding periods is just as important as the interest rate.
Is there anyone who wouldn’t want to turn $48,000 into $1.17 million, even if it takes 40 years to do it? At what rate of interest compounded annually will an investment triple itself in a 8 years B 10 years?1 Answer. At a rate of interest of 3.86% compounded annually investment will be tripled.
How long will it take money to triple itself if invested at 8 compounded annually?The answer to the question is 14.3 years.
What annual rate of interest compounded continuously is required to triple an investment in 5 years?Thus, the interest rate should be 24.57%.
What rate of interest compounded annually is equivalent to the rate of interest of 8% compounded quarterly?There are four Quart arena here, So the rate of interest is given in the question is 8%,, So this is divided by 100 and the quarter is four. This is 4 1. This is equal to 0.082. So the effective rate of interest is 8.2%.
