Question

Mr Robert Lee wants to buy a new boat in two years’ time. He estimates the boat will cost $86,600 at that time. He wishes to deposit an equal sum of money into a BankEast Ltd savings account every two weeks for the next two years in order to accumulate enough money to purchase the boat. If the BankEast account is paying interest at a rate of 14% p.a. compounded annually, how much must Mr Lee deposit every two weeks?

a) $1,380 b) $1,400 c) $1,433 d) $1,448 e) $1,460

Answer 1

FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream	$      86,600.00
PMT = the dollar amount of each annuity payment	PMT
r = the effective interest rate (also known as the discount rate)	14.98%	((1+14%/26)^26)-1)
n = the number of periods in which payments will be made	2
i= nominal rate of interest	14.00%
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
86600=	PMT*((((1 + 14.98%) ^2) - 1) / 14%)
Annual payment=	86600/((((1 + 14.98%) ^2) - 1) / 14%)
Annual payment=	$      37,647.49
Biweekly payment=	$              1,448	37647.49/26

So option D is the right answer.