Question

Katekani is looking to buy a house and can afford a payment of R14 000.00 a month. If the house costs R1 500 000 and Jane can get a 20 year loan at 10.25% p.a. compounded monthly, how much must Jane give as a deposit to lower her payment to R14 000.00 a month?

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
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
Nominal Rate	10.25%
Compounding	Monthly
Effective rate=	((1+10.25%/12)^12)-1)
	10.746%
Monthly payment	14,000
Annual payment	168,000
PV of 20 years payment	= 168000 * (((1-(1 + 10.746%) ^- 20)) / 10.25%)
PV of 20 years payment	1,426,180
House Cost	1,500,000
Depost in beginning required=	1500000-1426180
Depost in beginning required=	73,820