You graduated from college and decided to attend law school. If you go to law school,...

You graduated from college and decided to attend law school. If you go to law school, you will be forced to incur $180,000 in student loans. The re-payment of the student loans will take place over the next ten years after you graduate. The current rate on student loans is 6% ARP (with monthly compounding).
1. How much in interest will you pay over the lifetime of the loan?
2. How much interest will save if you add an additional $150 to your monthly payment?

Solutions

Expert Solution

Calculating interest paid over the life time of loan

To find the interest paid over life time of loan, we need to find the monthly payment of loan

Loan = $180000, No of months of loan = 12 x no of years of loan = 12 x 10 = 120 months

Monthly rate of interest = APR with monthly compounding / 12 = 6% / 12 = 0.50%

We can find the monthly payment of loan using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get monthly payment of loan = 1998.3690

Total amount paid over life of loan = Monthly payment of loan x no of months = 1998.3690 x 120 = $239804.2800

Total interest paid over lifetime of loan = Total amount paid over life of loan - Loan = 239804.2800 - 1800000 = $59804.28

Hence Total interest paid over lifetime of loan = 59804.28

Calculating Interest saved

Additional monthly payment = $150

New monthly payment = Monthly payment + Additional monthly payment = $1998.3690 + 150 = $2148.3690

If the monthly payment is increased, then no of months to payoff the loan will be reduced. We can find the no of months of payoff loan with new monthly payment by using NPER function in excel

Formula to be used in excel: =NPER(rate,pmt,-pv)

Using NPER function in excel, we get get no of months to payoff loan = 108.8454 months

Total amount paid over life of loan = no of months x monthly loan payment = 108.8454 x 2148.3690 = 233840.0832

Total interest paid over life of loan = Total amount paid over life of loan - Loan = 233840.0832 - 180000 = 53840.0832

Total interest saved over life of loan = 59804.28 - 53840.0832 = $5964.1968

Answer: $5964.1968

jeff jeffy answered 2 hours ago

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