Question

You can save $2,000 per year for the next four years in an account earning 8 percent per year. How much will you have at the end of the fourth year if you make the first deposit today? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Future Value:

Answer 1

Here, the deposits will be same every year, so it is an annuity. And the deposits start at te beginning of each year, so it is an annuity due. We need to calculate the future value of annuity due by the following formula:

FVAD = (1 + r) * P * ((1 + r)n  - 1 / r)

where, FVAD is future value of annuity due, P is the periodical amount = $2000, r is the rate of interest = 8% and n is the time period = 4

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

FVAD = (1 + 8%) * $2000 * ((1 + 8%)4 - 1 / 8%)

FVAD = (1 + 0.08) * $2000 * ((1 + 0.08)4 - 1 / 0.08)

FVAD = (1.08) * $2000 * ((1.08)4 - 1 / 0.08)

FVAD = (1.08) * $2000 * ((1.36048896- 1) / 0.08)

FVAD = (1.08) * $2000 * (0.36048896 / 0.08)

FVAD = (1.08) * $2000 * 4.506112

FVAD = $9733.20

So, at the end of fourth year, we will have $9733.20