Question

If $2,000 is invested at 4% annual interest compounded quarterly, how long would it take for the account balance to reach $10,000? Round your answer to the nearest tenth.

Answer 1

40.4 years

Explanation:

Answer 2

40.2 years

Explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), in which n represents the number of compounding periods per year. In this case n = 4. Solve the following equation for t (years):

$10,000 = $2,000(1 + 0.04/4)^(4t):

This is equivalent to

5 = 1.01^(4t). Taking the natural logarithm of both sides, we get:

ln 5 = 4t·㏑ 1.01, or

ln 5 1.609

-------------- = t = -------------- = 40.2 years

4·ln 1.01 4(0.010)