Question

Marc received the proceeds from an inheritance on April 20. He wants to set aside enough on April 21 so that he will have $17,000 available on July 25 to purchase a car when the new models are introduced. If the current interest rate on 91- to 180-day deposits is 4.50%, what amount should he place in the term deposit? The interest is compounded monthly

Answer 1

Since it was compounded monthly, we would apply the formula for calculating compound interest which is expressed as

A = P(1 + r/n)^nt

where

A is the amount after t years

P is the initial amount or principal

r is the interest rate

n is the number of compounding periods in a year

t is the time in years

From the information given,

A = 17000

r = 4.5/100 = 0.045

n = 12 because it was compounded monthly

t = number of days between April 21 and July 25 = 95 days

Recall,

365 days = 1 year

95 days = 95/365 = 0.26

Substituting these values into the formula, we have

17000 = P(1 + 0.045/12)^12 x 0.26

17000 = P(1.00375)^3.12

P = 17000/(1.00375)^3.12

P = 16802.63

Principal = $16802.63