frank borrowed money from an online lending company to buy a fishing boat. he took out a personal, amortized…

frank borrowed money from an online lending company to buy a fishing boat. he took out a personal, amortized loan for $13,500, at an interest rate of 4.35%, with monthly payments for a term of 4 years. for each part, do not round any intermediate computations and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) find franks monthly payment. (b) if frank pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) if frank pays the monthly payment each month for the full term, find the total amount of interest he will pay.

frank borrowed money from an online lending company to buy a fishing boat. he took out a personal, amortized loan for $13,500, at an interest rate of 4.35%, with monthly payments for a term of 4 years. for each part, do not round any intermediate computations and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) find franks monthly payment. (b) if frank pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) if frank pays the monthly payment each month for the full term, find the total amount of interest he will pay.

Answer

Explanation:

Step1: Identify loan - related values

The loan amount $P = 13500$, the annual interest rate $r=4.35%=0.0435$, the number of years $t = 4$, and the number of payments per year $n = 12$.

Step2: Calculate the monthly interest rate

The monthly interest rate $i=\frac{r}{n}=\frac{0.0435}{12}=0.003625$. The total number of payments $m=nt=12\times4 = 48$.

Step3: Use the amortized - loan payment formula

The formula for the monthly payment of an amortized loan is $M=\frac{P\times i\times(1 + i)^m}{(1 + i)^m-1}$. Substitute the values: [ \begin{align*} M&=\frac{13500\times0.003625\times(1 + 0.003625)^{48}}{(1+ 0.003625)^{48}-1}\ &=\frac{13500\times0.003625\times(1.003625)^{48}}{(1.003625)^{48}-1} \end{align*} ] First, calculate $(1.003625)^{48}\approx1.18377$. [ \begin{align*} M&=\frac{13500\times0.003625\times1.18377}{1.18377 - 1}\ &=\frac{13500\times0.003625\times1.18377}{0.18377}\ &=\frac{13500\times0.004290}{0.18377}\ &=\frac{57.915}{0.18377}\ &\approx315.15 \end{align*} ]

Step4: Calculate the total amount repaid

The total amount repaid $A = M\times m$. Since $M\approx315.15$ and $m = 48$, then $A=315.15\times48=15127.20$.

Step5: Calculate the total interest paid

The total interest paid $I=A - P$. Since $A = 15127.20$ and $P = 13500$, then $I=15127.20-13500 = 1627.20$.

Answer:

(a) $$315.15$ (b) $$15127.20$ (c) $$1627.20$