Lesson Find the compounding rate of an ordinary annuity
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<H2>Find the compounding rate of an ordinary annuity</H2> <H3>Problem 1</H3>To save for retirement, Karla Harby put $500 each month into an ordinary annuity for 10 years. Interest was compounded monthly. At the end of the 10 years, the annuity was worth $84,608. What annual interest rate did she receive? <B>Solution</B> <pre> Use the formula for the future value of the ordinary annuity FV = {{{PMT*(((1+r)^n-1)/r)}}}, where r is the effective monthly rate of compounding, n the number of deposits ( = months, in this problem). Substitute the numbers 84608 = {{{500*(((1+r)^120-1)/r)}}}. Simplify {{{84608/500}}} = {{{((1+r)^120-1)/r}}}, or {{{((1+r)^120-1)/r}}} = 169.216. It is the equation, which you want to solve to find r. Use any online solver for transcendent equations, for example, at this site www.desmos.com/calculator The solution is r = 0.00549 as the effective monthly rate. So, the annual nominal rate is 0.00549*12 = 0.06588, or 6.588%. <<<---=== {{{highlight(highlight(ANSWER))}}}. <U>CHECK</U>. Substitute this value of annual nominal rate into the formula for the future value. You will get FV = {{{500*(((1+0.06588/12)^120-1)/((0.06588/12)))}}} = $84,607.76, which is close to the given value in the problem. </pre> My other lessons on Finance problems in this site are - <A HREF=https://www.algebra.com/algebra/homework/Finance/Problems-on-simple-interest-accounts.lesson>Problems on simple interest accounts</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Problems-on-discretely-compounded-accounts.lesson>Problems on discretely compounded accounts</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Problems-on-continuously-compounded-accounts-.lesson>Problems on continuously compounded accounts</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Find-future-value-of-an-Ordinary-Annuity.lesson>Find future value of an Ordinary Annuity</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Find-a-value-of-a-regular-deposits-for-an-Ordinary-Annuity.lesson>Find regular deposits for an Ordinary Annuity</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/How-long-will-it-takes-for-an-ordinary-annuity-to-get-an-assigned-value.lesson>How long will it take for an ordinary annuity to get an assigned value?</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Find-future-value-of-an-Annuity-Due-saving-plan.lesson>Find future value for an Annuity Due saving plan</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Regular-withdrawals-from-an-annuity-account.lesson>Regular withdrawals from an annuity account</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Ordinary-annuity-account-with-non-zero-initial-deposit-as-a-combined-total-of-two-accounts.lesson>Ordinary annuity account with non-zero initial deposit as a combined total of two accounts</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Annual-depositing-and-semi-annual-compounding-in-ordinary-annuity-saving-plan.lesson>Annual depositing and semi-annual compounding in ordinary annuity saving plan</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/21-add-Regular-withdrawals-from-a-compounded-account.lesson>Variable withdrawals from a compounded account (sinking fund)</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Present-value-of-an-ordinary-annuity-saving-plan.lesson>Present value of an ordinary annuity cumulative saving plan</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Starting-value-of-a-sinking-fund.lesson>Problems on sinking funds</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Accumulate-money-using-ordinary-annuity-then-spend-money-via-sinking-fund.lesson>Accumulate money using ordinary annuity; then spend money via sinking fund</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Calculating-a-retirement-plan.lesson>Calculating a retirement plan</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Accumulating-money-via-ordinary-annuity-and-sending-simultaneously-via-sinking-fund.lesson>Accumulating money via ordinary annuity and spending simultaneously via sinking fund</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Loan-problems.lesson>Loan problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Mortgage-problems.lesson>Mortgage problems</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Amortizing-a-debt-on-a-credit-card.lesson>Amortizing a debt on a credit card</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/One-level-more-complicated-non-standard-problems-on-ordinary-annuity-plans.lesson>One level more complicated non-standard problems on ordinary annuity plans</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/One-level-more-complicated-problems-on-sinking-funds.lesson>One level more complicated problems on sinking funds</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/One-level-more-complicated-non-standard-problems-on-loans.lesson>One level more complicated non-standard problems on loans</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Using-Excel-to-find-the-principal-part-of-a-certain-loan-payment.lesson>Using Excel to find the principal part of a certain loan payment</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Finance-problems-solved-using-Excel.lesson>Using Excel to find the interest part of a certain loan payment</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/Tricky-problems-on-present-values-of-annuities.lesson>Tricky problems on present values of annuities</A> - <A HREF=https://www.algebra.com/algebra/homework/Finance/OVERVIEW-of-my-lessons-on-Finance-section-in-this-site.lesson>OVERVIEW of my lessons on Finance section in this site</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-I. 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