Question

Upon graduation from​ college, Warren Roberge was able to defer payment on his ​$33 comma 000 student loan for 9 months. Since the interest will no longer be paid on his​ behalf, it will be added to the principal until payments begin. If the interest is 4.55​% compounded monthly​, what will the principal amount be when he must begin repaying his​ loan?

Answer 1

Answer:

The principal when he begins repaying the loan will be $34,143.45¢

Explanation:

To calculate what the principal amount will be by the time he commences repayment of his loan (nine months later), we would attempt using the compound interest formula. The formula for calculating compound interest:-

Fv = Pv × [1 + (r/n)]^(n×t)

Where Fv = future value

Pv = present value

r = rate of interest

n = number of times of compounding in a year.

With respect to the question:

Pv = 33,000

r = 4.55% = 0.0455

t = 9 months = 3/4 years/0.75years.

n = 12 (since compounding is monthly)

Substituting appropriately:-

Fv = 33,000 × [1 + (0.0455/12)]^(12×0.75)

Fv = 33,000 × (1 + 0.003792)^9

Fv = 33,000 × [(1.003792)^9]

Fv = 33,000 × 1.03465

Fv = $34,143.45¢(new principal)

The interest that would have accrued during that period is $34,143.45 - $33,000 = $1,143.45¢.

Since this interest will be added to the initial amount Warren borrowed, then the resulting principal by the time he begins repayment of the loan after deferring it for nine months will be $34,143.45¢

Answer 2

Answer: $ 34143.356

Explanation:

Solution

Compound interest A = P ( 1 + i )^ 9

Where i is the rate

Future value of the loan after 9 months

P = 33000, i = 4.55/100 = 0.0455÷12

n = 9

Substitute the values into the above formular

A = 33000 ( 1 + 0.0455/12)^9

A = $ 34143.356