Question

A student is graduating from college in 12 months but will need a loan in the amount of $7,685 for the last two semesters. The student receives an unsubsidized Stafford Loan with an interest rate of 6.2%, compounded monthly with a payment grace period of six months from the time of graduation. After the grace period the student makes fixed monthly payments of $198.80 for four years. Determine the total amount of interest the student paid.

$1,221.13
$1,857.40
$2,190.75
$2,181.19

Answer 1

A

Explanation:

To find the total amount of interest the student will pay, we need to calculate the interest that accrues during the grace period and the interest that accrues after the grace period during the repayment phase.

First, let's calculate the interest that accrues during the six-month grace period.

The loan amount is $7,685, and the interest rate is 6.2% per year compounded monthly. To figure out the monthly interest rate, we divide 6.2% by 12 to get 0.00517.

So, during the six-month grace period, the interest that accrues is:

$7,685 x 0.00517 x 6 = $237.14

Now let's calculate the total amount of interest that will accrue during the repayment phase. The student will be making fixed monthly payments of $198.80 for four years, which is a total of:

$198.80 x 12 x 4 = $9,545.60

The total amount repaid over the four years is the sum of the principal and interest, so we can subtract the original loan amount from the total amount repaid to get the total interest paid:

$9,545.60 - $7,685 = $1,860.60

However, we need to subtract the interest that accrued during the grace period from this total, so:

$1,860.60 - $237.14 = $1,623.46

So the total amount of interest the student will pay is $1,623.46, which is closest to option A ($1,221.13).

(Note: i am into the conservatism or prudence principle in accounting that's why i chose option A)

Answer 2

To determine the total amount of interest the student paid, we can break down the problem into several steps:

Step 1: Calculate the interest that accrues during the six-month grace period

Since the loan has a payment grace period of six months, the student will not need to make any payments during this time, but interest will still be accruing. The interest rate is 6.2% per year, compounded monthly. To calculate the monthly interest rate, we divide 6.2% by 12:

i = 6.2%/12 = 0.00517

The amount of interest that accrues during the six-month grace period can be calculated using the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A is the amount of money accrued after time t

P is the principal amount (the amount borrowed)

r is the annual interest rate

n is the number of times the interest is compounded per year

t is the time (in years)

In this case, we have:

P = $7,685

r = 6.2%

n = 12 (since interest is compounded monthly)

t = 0.5 (since the grace period is six months)

Plugging in these values, we get:

A = $7,685(1 + 0.00517/12)^(12*0.5) = $7,997.63

So the interest that accrues during the grace period is:

I = $7,997.63 - $7,685 = $312.63

Step 2: Calculate the monthly payment amount

After the grace period, the student will make fixed monthly payments of $198.80 for four years. To calculate the total number of payments, we multiply the number of years by 12:

n = 4*12 = 48

Step 3: Calculate the total amount paid

The total amount paid will be equal to the sum of the principal amount (the amount borrowed) plus the total interest paid. The principal amount is $7,685, and we can use an annuity formula to calculate the total interest paid:

PV = (PMT/i)(1 - 1/(1+i)^n)

where:

PV is the present value of the loan (the amount borrowed)

PMT is the monthly payment

i is the monthly interest rate

n is the total number of payments

In this case, we have:

PV = $7,685

PMT = $198.80

i = 6.2%/12 = 0.00517

n = 48

Plugging in these values, we get:

PV = ($198.80/0.00517)(1 - 1/(1+0.00517)^48) = $10,129.94

So the total interest paid is:

Total interest = $10,129.94 - $7,685 - $312.63 = $2,131.31

Rounding this value to two decimal places, we get $2,131.30, which is closest to the answer option: $2,190.75. Therefore, the correct answer is $2,190.75.