what will be the value of the fund after three years?

Question

Megan is already looking ahead to graduation and a job, and she wants to buy a new car not long after her graduation. If after graduation she begins an investment program of $2,400 per year in an investment yielding 4 percent, what will be the value of the fund after three years? (Hint: Use Appendix A.3 or the Garman/Forgue companion website.) Round Future value of Series of Equal Amounts in intermediate calculations to four decimal places.

Answer 1

The question states that Megan will invest $2400/year for 3 years. Therefore, the value in her account at the end of 3 years will be sum of the 3 contributions of $2400, or $7200, plus earnings.

Let's look at two ways to find the actual value of the account after 3 years. First though, it's important to determine whether Megan will make her contributions at the beginning or end of each year. We can infer from the question that she'll have to earn the money after graduation before she can invest it, so that implies the contributions will be at the end of each year. The table provided in the appendix link confirms that assumption since it specifies in its title that it is for contributions at the end of the period.

To use the table, simply find the value at the intersection of 4% and 3 years, which is 3.1216. That's the annuity factor, and it tells us that a contribution of $1/period for 3 periods growing at 4%/period will grow to $3.1216. In this case, the contribution is $2400/period, so the value of Megan's savings will be $2400 * 3.1216 = $7,491.84.

If we did not have an annuity table handy, we could compute the value by examining the growth of each contribution:

1. The first contribution that Megan makes at the end of year 1 will grow 4% by the end of year 2 and then grow another 4% by the end of year 3:

End of Year 1: $2400

End of Year 2: $2400 * (1.04) = $2496.00

End of Year 3: $2496 * (1.04) = $2595.84.

(This is the same as the future value formula, FV = PV * (1+r)ⁿ, which in this case is $2400*(1.04)² = $2595.84)

1. At the end of year 2, Megan will contribute another $2400, which will grow at 4% to $2496 at the end of year 3.

1. Finally, at the end of year 3, Megan will contribute another $2400.

Summing up the future value of each payment, we get $2,595.84 + $2,496 + $2,400 = $7,491.84, which is the same result as with the annuity table.

I'd be happy to work through this together and address other questions you might have. To get in touch, just click on my photo above to go to my profile, and then click on the "Contact Cindy" button.

Answer 2

Hi Samantha,

The value of the fund after 3 years is:

$2,400 x (1.03) x (1.03) x (1.03)

Or in a general case:

Value of the fund after n years: (Initial Value)x(1+Yielding rate in %)^n

n= number of years

Hope it helps!

Francisco Lobato