Question

14. A mortgage requires you to pay $70,000 at the end of each of the next eight years. The interest rate is 8% a. What is the PV of these payments? b.Calculate for each year the loan balance that remains outstanding, the interest payment on the loan and the reduction in the loan balance.

Answer 1

Solution a
Calculation of loan amount
Annual payment	$              70,000
No of payments	8
Interest rate	8%
PV of annuity
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be calculated
PMT = the dollar amount of each annuity payment	$              70,000
r = the effective interest rate (also known as the discount rate)	8%
n = the number of periods in which payments will be made	8
PV of loan amount=	PMT x (((1-(1 + r) ^- n)) / r)
PV of loan amount=	70000* (((1-(1 + 8%) ^- 8)) / 8%)
PV of loan amount=	$      402,264.73
Solution b
Calculation of annual interest, amortization amount
Year	Beginning value	Interest @ 8%	Repayment	Closing balance
	A	B= A*8%	C	C= A+b-C
1	$      402,264.73	$    32,181.18	$     (70,000.00)	$ 364,445.90
2	$      364,445.90	$    29,155.67	$     (70,000.00)	$ 323,601.58
3	$      323,601.58	$    25,888.13	$     (70,000.00)	$ 279,489.70
4	$      279,489.70	$    22,359.18	$     (70,000.00)	$ 231,848.88
5	$      231,848.88	$    18,547.91	$     (70,000.00)	$ 180,396.79
6	$      180,396.79	$    14,431.74	$     (70,000.00)	$ 124,828.53
7	$      124,828.53	$      9,986.28	$     (70,000.00)	$   64,814.81
8	$        64,814.81	$      5,185.19	$     (70,000.00)	$             0.00