​$1000 is deposited in an account that pays an APR of 8.1% compounded annually. How long will it take for the balance to reach ​$100,000​?

Question

It will take _____ number of years to reach $100,000.

Answer 1

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

A = future amount = 100,000

p = principal = 1000

r = interest rate = 8.1/100 = 0.081

n = number times compounded per year = 1

t = time in years

 

100,000 = 1,000(1 + 0.081)^t

100 = 1.081^t

Take log of both sides

log100 = log1.081^t

2 = t(log1.081)

 

t = 2/(log 1.081) = 59.12665 years

 

(0.12665 years)(12 months per year) = 1.5 months

 

t = 59 years 1.5 months