Question

You need to save a total of $7,500 in order to buy a new motorcycle. You are starting with savings of $4,000 but will make no additional contributions. How long do you need to wait in order to reach your goal? In excel, compute the number of years required for annual interest rates of 2% to 10%, in two percent increments. What accurately depicts this calculation?

Answer 1

You do not need an excel spreadsheet to calculate this, you need to use the the future value formula:

future value = present value x (1 + r)ⁿ

present value = $4,000

future value = $7,500

so, (1 + r)ⁿ = $7,500 / $4,000 = 1.875

now we replace r:

for 2%)

1.02ⁿ = 1.875

n = log 1.875 / log 1.02 = 31.74 years

for 4%)

1.04ⁿ = 1.875

n = log 1.875 / log 1.04 = 16.03 years

for 6%)

1.06ⁿ = 1.875

n = log 1.875 / log 1.06 = 10.79 years

for 8%)

1.08ⁿ = 1.875

n = log 1.875 / log 1.08 = 8.17 years

for 10%)

1.1ⁿ = 1.875

n = log 1.875 / log 1.1 = 6.6 years

The higher the interest rate, the shorter it will take for you account to increase in value and the shorter you will have to wait in order to buy your motorcycle.