Annuities Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
You deposit \200attheendofeachmonthintoanaccountearning at the end of each month into an account earning 6\%annualinterestcompoundedmonthly.Howmuchwillyouhaveafter annual interest compounded monthly. How much will you have after 1$ year?

Solution

  1. 1
    This is an ordinary annuity. The future value formula is FV=Pโ‹…(1+r)nโˆ’1rFV = P \cdot \frac{(1+r)^n - 1}{r}.
  2. 2
    Monthly rate: r=0.0612=0.005r = \frac{0.06}{12} = 0.005. Number of payments: n=12n = 12.
  3. 3
    FV=200โ‹…(1.005)12โˆ’10.005=200โ‹…1.06168โˆ’10.005=200โ‹…0.061680.005FV = 200 \cdot \frac{(1.005)^{12} - 1}{0.005} = 200 \cdot \frac{1.06168 - 1}{0.005} = 200 \cdot \frac{0.06168}{0.005}.
  4. 4
    FV = 200 \cdot 12.336 = \2{,}467.20$.

Answer

$2,467.20\$2{,}467.20
An ordinary annuity involves equal payments made at the end of each period. The future value formula accounts for the fact that earlier payments earn more interest than later ones. The total deposits are \2{,}400,so, so \67.2067.20 is earned in interest.

About Annuities

A series of equal payments made at regular intervals over a fixed period of time. The future value and present value formulas calculate the total worth of these payment streams.

Learn more about Annuities โ†’

More Annuities Examples

Example 2 medium

What monthly payment is needed to accumulate [formula]50{,}000[formula]10[formula]4.8%$ annual inter

Example 3 medium

You want to receive [formula]1{,}000[formula]20[formula]5%$ annual interest compounded monthly. How

Example 4 hard

Compare an ordinary annuity and an annuity due, both with [formula]500[formula]6%[formula]5$ years.

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