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
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Ответ:
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 period10 years
Interest rate8%
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
Q2189.73
Ответ: