Question

1. Carla will give $200 to you every three months for 10 years (4x per year). At year 10 she will also give $10,000 to you. What amount of money must be available in her bank account in order for her to have enough money to meet her promise. The rate is 12%. Hint: this problem is a combination of 2 types of TVM problems. Your final answer is the sum of the two.

2. Brett has contract that will pay him $10,000 at the end of 5 years. Brett wants money now and not in 5 years, so he is willing to have contract signed over to you (so you would receive that money) if you give him some money today. If you require a 12% interest rate on money you lend to friends. What is the maximum amount you would you be willing to pay for this contract

Answer 1

Solution 1
First, we should calculate the future value of an annuity of regular quarterly payments
FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	To be calculated
PMT = the dollar amount of each annuity payment	200
r = the effective interest rate (also known as the discount rate)	12.00%	3.00%
n = the number of periods in which payments will be made	10*4	40
FV of quarterly payments=	PMT x ((((1 + r) ^ n) - 1) / r)
FV of quarterly payments=	200* ((((1 + 3%) ^ 40) - 1) / 3%)
FV of quarterly payments=	$ 15,080.25
Lump sum payment at T10=	$ 10,000.00
Total amount available in account after 10 years=	$ 25,080.25
Solution 2
Amount to be received after 5 years	$ 10,000.00
Time horizon in years	5.00
Interest rate	12%
The amount which can be lent is the present value of 10,000 @ 12% for 5 years.
Amount to be lent=	Amount after 5 years/(1+Interest rate)^time in years
Amount to be lent=	10000/(1+12%)^5
Amount to be lent=	$   5,674.27