Question

For an ordinary annuity with five annual payments of $100 and a 10% interest rate, how many years will the first payment earn interest? What will this payment's value be at the end? (I understand the formula portion but I do not understand how we come to the answer of 4 years for the first question. I need a break down of that please).

Answer 1

Solution :-

For an ordinary annuity with five annual payments of $100 the amount will be paid at the end of year so

First Payment is made at the end of first year and last Payment is made at the end of 5th Year and the time is of also 5 years

So the interest on 1st payment is earned from the end of first year to end of 5th year

Now you calculate the Difference 5 - 1 = 4

Therefore the first payment will earn interest for 4 years

The Payment Value at the end of 5th year =

= $100 * (1 + 0.10)⁴ + $100 * (1 + 0.10)³ + $100 * (1 + 0.10)² + $100 * (1 + 0.10) + $100

= ( $100 * 1.464 ) + ( $100 * 1.331 ) + ( $100 * 1.21 ) + ( $100 * 1.1 ) + $100

= $610.51

If there is any other doubt please ask in comments

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