Question

Huai takes out a $3,600 student loan at 6.6% to help him with 2 years of community college. After finishing the 2 years, he transfers to a state university and borrows another $11,600 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 has an interest rate of 7.3%. Find Huai’s monthly payment when regular payments begin.
Calculate the monthly payment on loan 1 (community college) round your answer two decimal places.

Calculate the monthly payment on loan 2. Round your answer two decimal places.

Answer 1

Answer:

a. The monthly payment on loan 1 is $76.03.

b. The monthly payment on loan 2 is $411.69.

Explanation:

a. Calculate the monthly payment on loan 1.

To determine the amount of periodic payments, the present value of annuity formula should be used:

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

Where:

PV= present value

p=periodic payment

i=rate of interest

n=number of periods

We get the data for this exercise:

PV= 3,600 (loan).

p= unknown (we must find this value)

i= 6.6% or 0.066. However, because we need to know the monthly payment, the interest rate should be divided by 12 (0.066 / 12).

n= 4 years and 7 months, that is 55 months.

And we replace in the formula:

$3600=P(\frac{1-(1+\frac{0.066}{12})^{-55} }{\frac{0.066}{12} } )$

$3600=P(\frac{1-(1+0.055)^{-55} }{0.0055} )$

$3600=P(\frac{1-(0.7395812268)}{0.0055} )$

$3600=P(\frac{0.2604187732}{0.0055} )$

$3600=P(47.348867)$

Therefore:

$P=\frac{3600}{47.348867}$

$P=76.03$

The monthly payment on loan 1 is $76.03.

b. Calculate the monthly payment on loan 2.

We get the data for this exercise:

PV= 11,600 (loan 2).

p= unknown (we must find this value)

i= 7.3% or 0.073. However, because we need to know the monthly payment, the interest rate should be divided by 12 (0.073 / 12).

n= 2 years and 7 months, that is 31 months.

And we replace in the formula:

$11600=P(\frac{1-(1+\frac{0.073}{12})^{-31} }{\frac{0.073}{12} } )$

$11600=P(\frac{1-(1+0.006083)^{-31} }{0.006083} )$

$11600=P(\frac{1-(0.8286047296)}{0.006083} )$

$11600=P(\frac{0.1713952704}{0.006083} )$

$11600=P(28.1761088936)$

Therefore:

$P=\frac{11600}{28.1761088936}$

$P=411.69$

The monthly payment on loan 2 is $411.69.