Question

A borrower has obtained a 25-year, $2,500,000 loan at 5% with monthly payments from Bank A. Ten years later, Bank B wants to purchase the mortgage from Bank A and Bank B wants to get at least 6% return from the purchase. How much would Bank B be willing to pay for the loan?

a) $1,538,918.3 b) $1,625,978.1 c) $1,731,899.4 d) $1,848,111.9

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	$      2,500,000
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	5.12%	((1+5%/12)^12)-1)
i=nominal Interest rate	5.00%
n = the number of periods in which payments will be made	25
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / i)
2500000=	Annual payment* (((1-(1 + 5.12%) ^- 25)) /5%)
Annual payment=	$    175,377.01
After 10 years, Bank purchased this loan so PV of all remaining 15 years payment @ 6% should be computed
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$    175,377.01
r = the effective interest rate (also known as the discount rate)	6.17%	((1+6%/12)^12)-1)
i=nominal Interest rate	6.00%
n = the number of periods in which payments will be made	15
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / i)
PV of annuity=	175377.01* (((1-(1 + 6.17%) ^- 4)) /6%)
PV of annuity=	$   1,731,899.4