How long will it take for the following deposits to reach $8,000? a) $6,000 at 3.5% per year compounded quarterly.

Answer 1

F = P(1 + r/n)^nt

F = future value

P = present value

r = annual interest rate

n = number of payments per year (compounding period)

8000 = 6000(1 + 0.035/4)^4t

1.3333 = (1.00875)^4t

Taking log of both sides:

ln(1.3333) = 4t*ln(1.00875)

Solving for t:

t = (1/4) * ln(1.3333)/ln(1.00875) = 8.255 years (about 8 years, 3 months, 2 days)