Question

1. Solve the following equations which involve cash flows.

a. A student is trying to value an internship opportunity for the upcoming summer. The internship will last three months and pay her $2,111.00 at the end of each month. She will also get a “signing” bonus at the beginning of the internship for $525.00. If the student can invest this money in an account that pays 5.76% APR with monthly compounding, what is the value of her account at the end of her internship?

b. A relative has promised to pay you $99.00 today, and he will pay you additional payments every year for the next five years. Each year he will add $76.00 to the previous payment. (So, the payment in year 1 will equal $175.00). You decide to save every dollar you are given and will invest the money in an account paying 5.00% annual interest. How much money will you have accumulated in five years? Keep in mind that you will have six total cash flows to invest.

Answer 1

Solution a

The internship generates the following cash flows

Month	Cash flow
0	$525.00
1	$2,111.00
2	$2,111.00
3	$2,111.00

To calculate the value of the cash flows at the end of the internship, we will calculate future value of all the cash flows.

To calculate future value (FV), the cash flows will be multiplied with FV factor:

FV factor = (1+ R)^t

R= 5.76%/12 = 0.48%

Month	Cash flow	FV Factor 0.48%	FV
0	$525.00	1.014469	$532.60
1	$2,111.00	1.009623	$2,131.31
2	$2,111.00	1.0048	$2,121.13
3	$2,111.00	1	$2,111.00
		Total	$6,896.04

Therefore, the value of the cash flows at the end of internship would be $6,896.04.