7. You take out a student loan of $20,000. The deal is that for the next 5 years
ID: 3148677 • Letter: 7
Question
7. You take out a student loan of $20,000. The deal is that for the next 5 years you make no payments and you are charged a simple interest of 3.5%. After 5 years you have to pay back the balance over the next 5 years in monthly installments at an interest rate of 4.8% (monthly compounding, of course):
(a) What is the balance after the first 5 years?
(b) What will your monthly payments be?
(c) What is the balance you owe after one year of payments?
(d) What is the total interest that this loan wi1l cost you by the time it's paid off?
Explanation / Answer
(a)
Calculate the balance after using simple interest formula
principal = $20,000
t = 5 years
interest rate = 3.5%
interest = PRT = 20000*5*0.035 = 3500
balance - 20000+3500 = 23500
(b)
The mathematical formula for calculating EMIs is:
EMI = [P x R x (1+R)^N]/[(1+R)^N-1],
where P stands for the loan amount or principal = 23500
R is the interest rate per month = 4.8%/12 monthly = 0.4% = 0.004, t
N is the number of monthly instalments = 5*12 = 60
EMI = [23500x 0.004 x (1+0.004)^60]/[(1+0.004)^60-1]
EMI = $441.32
(c)
total amount to be paid = EMI*60 = $26,479.44
paid after one year = EMI*12 = $5,295.89
balance = total to be paid - paid after one year = $21183.55
(d)
Total interest paid = $26,479.44 - $20,000 = $6479.44
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