Question

When you take your first job, you decide to start saving right away for your retirement. You put $5,000 per year into a saving plan, which interest rate 10% per year. Five years later, you move to another job and stop making contributions to the saving plan. If the first plan continued to earn interest for another 35 years, determine the future worth in year 40.

		$81,954
		$89,154
		$857,840
		$859,840

Answer 1

Option (c) is correct

First we will calculate the value of savings plan after 5 years as below:

Here, the deposits will be same every year, so it is an annuity. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $5000, r is the rate of interest = 10% and n is the time period = 5

Now, putting these values in the above formula, we get,

FVA = $5000 * ((1 + 10%)⁵ - 1 / 10%)

FVA = $5000 * ((1 + 0.10)⁵ - 1 / 0.10)

FVA = $5000 * ((1.10)⁵ - 1 / 0.10)

FVA = $5000 * ((1.61051- 1 / 0.1)

FVA = $5000 * (0.61051/ 0.1)

FVA = $5000 * 6.1051

FVA = $30525.5

So, after 5 years, savings plan will have $30525.5

Now, we will calculate the value of savings plan after another 35 years as per below:

Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value, PV = Present value = $30525.5, r = rate of interest = 8%, n= time period = 35

now, putting theses values in the above equation, we get,

FV = $30525.5 * (1 + 10%)³⁵

FV = $30525.5 * (1 + 0.10)³⁵

FV = $30525.5 * (1.10)³⁵

FV = $30525.5 * 28.1024368481

FV = $857840

So, future worth in 40 years will be $857840.