Question

Suppose $5,000 is invested in a quarterly compounding account at 6%. Approximately how long will it take for the account to reach $6,750?
a. 5 years
b. 12 years
c. 4 years
d. 6 months

Answer 1

Using:
P = invested amount
r = annual rate of interest
t = number of years
A = amount of money accumulated after n years, including interest
n = number of times the interest is compounded per year

The formula is: \[A=P(1+r/n)^{nt}\]
\[6,750 = 5,000(1+(0.06/4))^{4t}\]Solve for t:
\[6750/5000 = 1.015^{4t}\]\[1.35 = 1.015^{4t}\]Now take the log of both sides and isolate t:

If I'm not too rusty on logs, I end up with ~20 = 4t so t = 5 (years)