Question

Mark Johnson saves a fixed percentage of his salary at the end of each year. This year he saved $2,000. For each of the next 5 years, he expects his salary to increase at an 4% annual rate, and he plans to increase his savings at the same 4% rate. There will be a total of 6 investments, the initial $2,000 plus five more. If the investments earn a return of 15% per year, how much will Mark have at the end of six years

Answer 1

Mark will have $19,878.70 at the end of six years

Step-by-step explanation:

Use the following formula to calculate the present value of cash flows

PV =
`A [(1 - ((1+g)/(1+r))^n )/(r - g) ]`

Where

A = Investment = $2,000

g = growth rate = 4%

r = 15%

n = 6

Placing values in the formula

PV =
`2,000 [(1 - ((1+0.06)/(1+0.15))^6 )/(0.15 - 0.06) ]`

PV = $8,594.11

Now calculate the future value in order to determine the amount Mark will have at the ned of six years

Future value =
`PV ( 1 + r )^n`

Where

PV = $8,594.11

r = 15%

n = 6

Placing values in the formula

Future value =
`8,594.11 ( 1 + 0.15 )^6`

Future value = $19,878.70