Mark Johnson saves a fixed percentage of his salary at the end of each year. This year he saved $2,500. For each of the next 5 years, he expects his salary to increase at an 10% annual rate, and he plans to increase his savings at the same 10% rate. There will be a total of 6 investments, the initial $2,500 plus five more. If the investments earn a return of 13% per year, how much will Mark have at the end of six years

Mark will have at the end of six years the amount of $25,865.74

Explanation:

According to the given data we have the following:

First investment = 2500

Investment increasing at rate of 10%

Interest rate = 13%

t=6 years

Present value is given by formula = C * [ ((1+g) ^n / (1+i) ^n) - 1 ] / (g-i)

C is first value = 2,500

g is increase in investment = 0.10

i is intrest rate = 0.13

n is no of years = 6

Putting values into the equation

P = 2500 * [ ((1 + 0.10) ^6 / (1+0.13) ^6) - 1 ] / (0.10-0.13) 1.771561 2.08195

P = 2500 * [ ((1.10) ^6 / (1.13) ^6) - 1 ] / (-0.03)

P = 2500 * [0.8509142870866 - 1 ] / (-0.03)

P = 2500 * (-0.14908571) / (-0.03)

P = 2500 * 4.9695236

P=$12,423.809

Future value = P * (1+i) ^t

= $12,423.809 * (1+0.13) ^6

= $25,865.74

Mark will have at the end of six years the amount of $25,865.74