Question

Amishi deposited $400 at the end of each six months for 19 years in a savings account. If the account paid 4% interest, compounded semi annually, use the appropriate formula to find the future value of her account. (round your answer to the nearest sent.)

Answer 1

Here, the deposits will be same every semi annual year, so it is an annuity.Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $400, r is the rate of interest = 4% compounded semi annually, so semi annual rate = 4% / 2 = 2% and n is the time period = 19 * 2 = 38 semi annual years

Now, putting these values in the above formula, we get,

FVA = $400 * ((1 + 2%)³⁸ - 1 / 2%)

FVA = $400 * ((1 + 0.02)³⁸- 1 / 0.02)

FVA = $400 * ((1.02)³⁸ - 1 / 0.02)

FVA = $400 * ((2.1222987924- 1 / 0.02)

FVA = $400 * (1.1222987924/ 0.02)

FVA = $400 * 56.11493962

FVA = $22445.98

So, future value is $22445.98.