Question

Rachael Steele wants to borrow $6,000 for a period of four years. She has two choices. Her bank is offering to lend her the amount at 7.25 percent compounded annually. She can also borrow from her firm and will have to repay a total of $8,130.93 at the end of four years. Based on the information provided, which of the following is true?

A:She should borrow from her firm as it is charging a lower interest of 7%.

B: She should borrow from the firm as it is charging a lower interest rate of 6%.

C: She should borrow from the bank as her firm is charging a higher interest of 7.89%.

D:She should borrow from the bank as her firm is charging a higher interest of 9.70%.

Answer 1

The rate of interest the firm must be charging can be determined with help of below formula-

A = P ( 1 + r )ⁿ

where,

A = Future amount (ending amount)

P = Initial amount

r = rate of interest

n = No. of years.

She wants to borrow $6,000, hence, P = $6,000

She will have to repay a total of $8,130.93, hence, A = $8,130.93

n = 4 years

We have to calculate r .

A = P ( 1 + r )ⁿ

8,130.93 = 6,000 ( 1 + r ) ⁴

8,130.93 / 6,000 = ( 1 + r ) ⁴

1.355155 = ( 1 + r ) ⁴

Taking, the 4th under root of 1.355155

1.07893987273584 = 1 + r

r = 1.07893987273584 - 1

r = 0.078939873

= 7.894 % (approx)

The firm must be charging annual rate of 7.894 % where as the bank is offering to lend her the amount at 7.25 percent compounded annually.

Bank rate is less hence, She should borrow from the bank as her firm is charging a higher interest of 7.89%.

Correct answer is C.

Hope it helps!