Question

Huai takes out a $2900 student loan at 6.2% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and borrows another $12,500 to defray expenses for the 5 semesters he needs to graduate. He graduates 4 years and 4 months after acquiring the first loan and payments are deferred for 3 months after graduation. The second loan was acquired 2 years after the first and had an interest rate of 7.9% . Find the total amount of interest that will accrue until payments begin.

Answer 1

1- Student takes out a loan of $2900 student loan with a interest rate 6.2% .

interest rate 6.2% = 0.062

2- After finishing the 2 years, he borrows another $12,500 to defray expenses for the 5 semesters he needs to graduate

3-He graduates 4 years and 4 months after acquiring the first loan and payments are deferred for 3 months after graduation.

4-The second loan was acquired 2 years after the first and had an interest rate of 7.9% .

interest rate 7.9% = 0.079

5- Formula for present value of annuity:

$PV=P\cdot(\frac{1-(1+i)^{-n}}{i})$

where:

PV= 2900

p=periodic payment

i=0.062

n=number of periods= 4 years and (4 +3) month= 4*12+7=48+7=55

$2900=P\cdot(\frac{1-(1+\frac{0.062)}{12}^{-55}}{\frac{0.062}{12}})$$\begin{gathered} 2900=P(47.7693) \\ P=\frac{2900}{47.7693}=60.7084 \end{gathered}$

The monthly payment for the first loan is $60.7084. In 55 months, we have: $ 3338.962

Now for loan 2

PV= 12500

p=periodic payment

i=0.079

n=number of periods= 2 years and (4 +3) month= 2*12+7=24+7=31

$12500=P\cdot(\frac{1-(1+\frac{0.079)}{12}^{-31}}{\frac{0.079}{12}})$$12500=P(27.9585)$$P=\frac{12500}{27.9585}=447.0912$

The monthly payment for the second loan is $447.0912. In 31 months, we have: $ 13859.8272

The exercise ask the total amount of interest that will accrue until payments begin.

13859.8272+ 3338.962=$17198.7892