Toby just graduated from four years of college. at the beginning of each year, he took out a stafford loan with a principal of $6,125. each loan had a duration of ten years and an interest rate of 5.3%, compounded monthly. all of the loans were subsidized. toby plans to pay off each loan in monthly installments, starting from his graduation. what is the total lifetime cost for toby to pay off his 4 loans? round each loan's calculation to the nearest cent

$31616.156

Explanation:

Given:

Each year Toby took a loan of $6,125

Therefore,

The total amount after 4 years = 4 × $6,125 = $24,500

Rate of interest = 5.3%

Number of years, n = 10

Now,

The present value of an annuity to find the monthly payments can be calculated as:

Present value = Monthly payment ×

r is the rate

K when compounded monthly = 12

on substituting the respective values, we get

$24,500 = Monthly payment × [tex][\frac{(1-(1+\frac{0.053}{12})^{-12\times10})}{(\frac{0.053}{12})}]

or

$24,500 = Monthly payment × 92.99

or

Monthly payment = $263.46

Now, Total value of monthly payment after 10 years = $263.46 × 12 × 10

= $31616.156