Question

Find the future values of these ordinary annuities. Compounding occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent. $600 per year for 16 years at 16%. $   $300 per year for 8 years at 8%. $   $900 per year for 14 years at 0%. $   Rework parts a, b, and c assuming they are annuities due. Future value of $600 per year for 16 years at 16%: $   Future value of $300 per year for 8 years at 8%: $   Future value of $900 per year for 14 years at 0%: $

Answer 1

Formula for Future Value of Annuity is:

Where,
FVA = Future Value of Annuity
A = Annuity
i = rate of interest
n = number of years

a). $600 per year for 16 years at 16%.

i=16% or 0.16 in decimal form.

Substituting the values, we get:

Therefore, $600 per year for 16 years at 16% make your investment  $36,555.02

b).$300 per year for 8 years at 8%.

c). $900 per year for 14 years at 0%.

When interest rate is 0%, you will only get what you invested over the years. Therefore, using the formula makes no sense here. So we can simply multiply the number of payments and amount per year to get the answer.

ie.

d). When all the above annuities are annuities due, that means the payment at beginning of the period.

Here, there is a small modification to the formula we used above. i.e you have to multiply the formula with (1+i).

i) Future value of $600 per year for 16 years at 16%

ii) Future value of $300 per year for 8 years at 8%.

ii)Future value of $900 per year for 14 years at 0%.

When interest rate is 0%, it doesn't matter whether you invest in the beginning or at the end. You will only get what you invested. i.e FVA = 900 * 14 = $12,600.00