Annuities Math Example 4

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

Example 4

hard
Compare an ordinary annuity and an annuity due, both with \500monthlypaymentsat monthly payments at 6\%annualinterestcompoundedmonthlyfor annual interest compounded monthly for 5$ years. How much more does the annuity due accumulate?

Solution

  1. 1
    Ordinary annuity: FV = 500 \cdot \frac{(1.005)^{60} - 1}{0.005} = 500 \cdot \frac{1.34885 - 1}{0.005} = 500 \times 69.770 = \34{,}885.02$.
  2. 2
    Annuity due: FV_{\text{due}} = FV_{\text{ordinary}} \times (1 + r) = 34885.02 \times 1.005 = \35{,}059.44.Difference:. Difference: \35{,}059.44 - \34{,}885.02 = \174.42174.42.

Answer

$174.42 more with annuity due\$174.42 \text{ more with annuity due}
An annuity due makes payments at the beginning of each period instead of the end, so each payment earns one extra period of interest. The future value of an annuity due equals the ordinary annuity future value multiplied by (1+r)(1 + r). The difference grows larger with higher interest rates or longer time periods.

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 →

More Annuities Examples

Example 1 easy

You deposit [formula]200[formula]6%[formula]1$ year?

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

← All Annuities Examples Annuities Concept