Question

Angela will need $2000 in three years so that she can take a cruise vacation with some of her friends. She just received a large income tax refund of $2500 and would like to invest part of that money in a CD that will result in $2000 after three years. If the interest rate on the CD is 2% compounded quarterly, how much should Angela invest in the CD?

Answer 1

$1,883.81

Step-by-step explanation:

To calculate this, we use the formula for calculating the present value (FV) as follows:

PV = FV ÷ (1 + r)^n ……………………………………………. (1)

PV = Present value or the amount to invest in the CD = ?

FV = future value or the amount needed in three years = $2,000

r = interest rate = 2% annually = 2%/4 quarterly = 0.5% or 0.005 quarterly

n = number of period = 3 years = (3 × 4) quarters = 12 quarters

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

PV = 2,000 ÷ (1 + 0.005)^12 = 2,000 ÷ 1.0616778118645 = $1,883.81

Therefore, Angela should invest $1,883.81 in the CD.