Question

1) Today you borrow 12,000 for 5 years. The bank lends you this money with an interest rate of 7%. What would be the interest expense each year on this fully amortized loan?

2) You are in the leasing business and have 20,000 asset to lease. If you require a 12% return on your asset, and the lease term is 9 years, how much would the lease payment be at the beginning of each year?

Answer 1

1) First of all , lets find Yearly installments

Yearly installments = Loan/PVIFA(r%,n)

r = rate of interest = 7%

n = no. of years = 5

Loan amount = $12000

PVIFA(r%,n) = [1-(1/(1+r)^n / r ]
PVIFA(7%,5) = [1-(1/(1+7%)^5 / 7%]
=[1-(1/(1+0.07)^5 / 0.07]
=[1-(1/(1.07)^5 / 0.07]
=[1-0.7130 / 0.07]
=0.2870/0.07
=4.10020
Thus Yearly installments = 12000/4.10020
= 2926.69 $

Amortization schedule

			Towards
Year	Opening balance	Installmets	Interest @ 7%	Principal	Closing balance
	A	B	C = A x 7%	D = B-C	E = A - D
1	12000.00	2926.69	840.00	2086.69	9913.31
2	9913.31	2926.69	693.93	2232.76	7680.55
3	7680.55	2926.69	537.64	2389.05	5291.50
4	5291.50	2926.69	370.41	2556.28	2735.22
5	2735.22	2926.69	191.47	2735.22	0.0

Thus interest expense every year

Year	Interest @ 7%
1	840.00
2	693.93
3	537.64
4	370.41
5	191.47

2) Here formula of present value of annuity due will be used

Lease payment required = Asset value / [PVIFA(r%,n) x (1+r)]

r = rate of interest = 12%

n = no. of years = 9

Asset value = $20000

PVIFA(r%,n) = [1-(1/(1+r)^n / r ]
PVIFA(12%,9) = [1-(1/(1+12%)^9 / 12%]
=[1-(1/(1+0.12)^9 / 0.12]
=[1-(1/(1.12)^9 / 0.12]
=[1-0.3606 / 0.12]
=0.6394/0.12
=5.3282
Thus Lease payment required = 20000/ [5.3282 x 1.12]
= 20000/5.9676

= 3351.41 $