Question

You wish to accumulate a total of $ 63,226 for a special purpose exactly 11 years from now. You will make deposits quarterly, with the first one exactly 8 quarters from now and the last one exactly 11 years from now. The savings rate is 10.94 % compounded quarterly. How much total interest does the bank contribute towards your accumulation?

Answer 1

First, we calculate the quarterly deposit.

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. We need to calculate this.

r = periodic rate of interest. This is (10.94%/4). We divide by 4 since we need to convert the annual rate into quarterly rate)

n = number of periods. This is 37. (There are 37 quarterly deposits made)

$63,226 = P * [(1 + (10.94%/4))³⁷ - 1] / (10.94%/4)

P = $63,226 * (10.94%/4) / [(1 + (10.94%/4))³⁷ - 1]

P = $1,008.99

Total amount deposited = quarterly deposit * total number of deposits

Total amount deposited = $1,008.99 * 37 = $37,332.62

Total interest earned from bank = amount accumulated at end - total amount deposited

Total interest earned from bank = $63,226 - $37,332.62

Total interest earned from bank = $25,893.38