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A student takes out a $10,000, 10-year loan with two possible repayment plans, (i) immediate repayment or (ii) a grace period during the college years. The student takes 5 years to graduate. The interest rate is 8%, compounded annually and the loan is paid off as a yearly lump sum. Since the bank is a for-profit business (beholden to its shareholders and required to maximize profit), the bank intends to receive the same return on this loan either way. How much are the annual payments under option (i) and option (ii)?

A. (i) $1,490 and (ii) $2,189
B. (i)$2,876and (ii) $3,010
C. (i) $2,189 and (ii) $2,254
D. (i) $2,254 and (ii) $2.876

Respuesta :

Answer:

Annual repayment under option(i) is $1490

Annual repayment under option (ii) is $2189

Therefore option A is correct

Explanation:

Immediate repayment  

Loan amount $10,000  

Repayment period 10 years

Interest rate 8%

Let the annual repayment be X  

:10000=X*(1/0.08)*(1-(1/(1.08)^10))  

1/0.08 = 12.5

1-(1/(1.08)^10 = 0.536806512

12.5*0.536806512 =6.710081399

10000=X*6.710081  

X = $1,490.29  

 

5 years grace period  

let  P be accummulated loan value after 5 year  

P=10000*(1.08)^5 =14693.28077

Let annual repayment be Q  

14693.28=Q*(1/0.08)*(1-(1/(1.08)^10))  

1/0.08 =          12.5

1-(1/(1.08)^10 =  0.536806512

12.5*0.536806512    =6.710081399

14693.28=Q*6.710081  

Q 2189.73

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