Question

You plan to make five deposits of $1,000 each, one every 6 months, with the first payment being made in 6 months. You will then make no more deposits. If the bank pays 4% nominal interest, compounded semiannually, how much will be in your account after 3 years? Round your answer to the nearest cent.

Answer 1

You will have $5,204.04 in your account after 3 years.

Step-by-step explanation:

To calculate this, the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = M × {[(1 + r)^n - 1] ÷ r} ................................. (1)

Where,

FV = Future value of the amount after 3 years =?

M = Payment every 6 months = $1,000

r = Semiannual interest rate = 4% ÷ 2 = 2%, 0.02

n = number of times the payment is made = 5

Substituting the values into equation (1), we have:

FV = 1,000 * {[(1 + 0.02)^5 - 1] / 0.02}

FV = 1,000 * {[1.02^5 - 1] / 0.02}

FV = 1,000 * {[1.1040808032 - 1] / 0.02}

FV = 1,000 * {0.1040808032 / 0.02}

FV = 1,000 * 5.20404016

FV = 5,204.04016 = $5,204.04 to the nearest cent.

Therefore, you will have $5,204.04 in your account after 3 years.