How long will it take for $2100 to grow to $42,600 at an interest rate of 3.2% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Question

How long will it take for $2100 to grow to $42,600 at an interest rate of 3.2% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

Answer 1

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

ln(A/P) = ntln(1+r/n)

t = ln(A/P)/(n ln(1+r/n))

A= 42600

P=2100

n=4

r = 0.032

t = ln(42600/2100)/(4(1+0.032/4)) ≈ 94.44 years