when kira bought her house, she got her mortgage through an online lending company. the mortgage was a…

when kira bought her house, she got her mortgage through an online lending company. the mortgage was a personal, amortized loan for $98,000, at an interest rate of 5.55%, with monthly payments for a term of 40 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 kiras monthly payment. (b) if kira pays the monthly payment each month for the full term, find her total amount to repay the loan. (c) if kira pays the monthly payment each month for the full term, find the total amount of interest she will pay.

when kira bought her house, she got her mortgage through an online lending company. the mortgage was a personal, amortized loan for $98,000, at an interest rate of 5.55%, with monthly payments for a term of 40 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 kiras monthly payment. (b) if kira pays the monthly payment each month for the full term, find her total amount to repay the loan. (c) if kira pays the monthly payment each month for the full term, find the total amount of interest she will pay.

Answer

Explanation:

Step1: Identify the loan - related values

The loan amount $P = 88000$, the annual interest rate $r=5.55%=0.0555$, the number of years $n = 40$, and the number of payments per year $m = 12$.

Step2: Calculate the monthly interest rate

The monthly interest rate $i=\frac{r}{m}=\frac{0.0555}{12}=0.004625$.

Step3: Calculate the total number of payments

The total number of payments $t=n\times m=40\times12 = 480$.

Step4: Use the formula for the monthly payment of an amortized loan

The formula for the monthly payment $M$ of an amortized loan is $M = P\times\frac{i(1 + i)^t}{(1 + i)^t-1}$. Substitute the values: [ \begin{align*} M&=88000\times\frac{0.004625(1 + 0.004625)^{480}}{(1+ 0.004625)^{480}-1}\ \end{align*} ] Let $x=(1 + 0.004625)^{480}$. [ \begin{align*} x&=1.004625^{480}\ &\approx8.0797 \end{align*} ] [ \begin{align*} M&=88000\times\frac{0.004625\times8.0797}{8.0797 - 1}\ &=88000\times\frac{0.037368}{7.0797}\ &=88000\times0.005278\ &\approx464.46 \end{align*} ]

Step5: Calculate the total amount to repay the loan

The total amount to repay the loan $A = M\times t$. $A=464.46\times480 = 222940.80$.

Step6: Calculate the total amount of interest

The total amount of interest $I=A - P$. $I=222940.80-88000=134940.80$.

Answer:

(a) $$464.46$ (b) $$222940.80$ (c) $$134940.80$