Question

A company received a loan of $39,000 from a bank that was charging interest at a rate of 4.92% compounded quarterly.a. Calculate the accumulated amount of this loan at the end of 9 years and 3 months._________________Round to the nearest centb. Calculate the interest charged on this loan._________________Round to the nearest cent

Answer 1

Given:

Loan amount = $39,000

Interest rate, r = 4.92% compounded quarterly.

Let's solve for the following:

• (a) Calculate the accumulated amount of this loan at the end of 9 years and 3 months.

To find the accumulated amount apply the formula:

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

Where:

A is the final amount

P is the loan amount = $39000

r is the interest rate = 4.92% = 0.0492

Since it is compounded quarterly, n = 4

t is the time in years = 9 years 3 months

To write the time in years, we have:

`9(3)/(12)=9(1)/(4)=\frac{37}{4\text{ }}years`

Therefore, to find the accumulated amount, we have:

`\begin{gathered} A=39000(1+(0.0492)/(4))^{4\ast(37)/(4)} \\ \\ A=39000(1+0.0123)^(37) \\ \\ A=39000(1.0123)^(37) \end{gathered}`

Solving further:

`\begin{gathered} A=39000(1.571960987) \\ \\ A=61306.48 \end{gathered}`

Therefore, the accumulated amount of this loan at the end of 9 years and 3 months is: $61,306.48

• (b) Calculate the interest charged on this loan.

To calculate the interest, subtract the principal amount from the accumulated loan.

We have:

Interest charged = Accumulated loan - Principal amount

Interest charged = $61,306.48 - $39,000

Interest charged = $22,306.48

Therefore, the interest chrged on this loan is $22,306.48

ANSWER:

• a) $61,306.48

,

• b) $22,306.48