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:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]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:
[tex]9\frac{3}{12}=9\frac{1}{4}=\frac{37}{4\text{ }}years[/tex]Therefore, to find the accumulated amount, we have:
[tex]\begin{gathered} A=39000(1+\frac{0.0492}{4})^{4\ast\frac{37}{4}} \\ \\ A=39000(1+0.0123)^{37} \\ \\ A=39000(1.0123)^{37} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} A=39000(1.571960987) \\ \\ A=61306.48 \end{gathered}[/tex]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
