Question

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

Answer 1

Answer:

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

Answer 2

Answer:

$29,228.47

Explanation:

year            savings                investment               total

                                               returns                                      

1                  $2,500                (1 + 13%)⁶                  $5,204.88

2                 $2,750                (1 + 13%)⁵                   $5,066.70

3                 $3,025                (1 + 13%)⁴                   $4,932.18

4                 $3,327.50           (1 + 13%)³                   $4,801.24

5                 $3,660.25          (1 + 13%)²                    $4,673.77

6                 $4,026.28           (1 + 13%)                    $4,549.70

total           $19,289.03                                          $29,228.47

Since Mark earns compound interest, then the returns will be:

• 1.13⁶ = 2.082
• 1.13⁵ = 1.8424
• 1.13⁴ = 1.6305
• 1.13³ = 1.443
• 1.13² = 1.2769
• 1.13¹ = 1.13