Question

Starting on September 1, 2000 - the day he starts college - and ending on September 1, 2004, Craig borrowed $4000 a year to pay for college expenses (i.e. that's 5 withdrawals total).
After graduation, he decided to go to graduate school in mathematics, and his loans were deferred (i.e. they accrued interest, but no payments were due). After finishing graduate school, he began repaying his loans. Beginning on July 1, 2007, he made monthly payments for 11 years. Each payment increased by 1.5% over the previous payment. If his loans had a fixed nominal rate of 6.6% convertible monthly for the entire life of the loans, what was the size of his first payment?

Answer 1

Amount acrued before his graduate school = FV(6.6%,4,4000,0,1) = 18820.07

No of months for graduation = 34

Thus, amount he's supposed to pay back on July 1st, 2007= 18820.07 * (1+6.6%/12)^34 = 22678.3672

He pays back this amount in 11 years = 132 months

After this use excel. Assume any amount to start with and increase payments by 1.5% every month for 132 months. Deduct the same amount from the total amount he is supposed to pay back (adjusted for monthly interest charges)

Thus, amount left = (Amount left a month ago - amount paid this month)*(1+yearly interest / 12)

Use solver to get the fisrt installment value by setting amount left after 132 months = 0 by changing the fisrt installment.

The fisrt installment comes out to be around $88