Stan put aside 10000 in an account with interest reinvested

Stan put aside $10,000 in an account with interest reinvested monthly at 2.5%. How long will It take for him to earn $2000? Round to the nearest tenth of a year.

Solution

The compound interest formula calculates the amount of interest earned on an account or investment where the amount earned is reinvested. By reinvesting the amount earned, an investment will earn money based on the effect of compounding.

Principal = $10,000 ; r = 2.5% ; compounding = monthly ; time t = ? Total earning = $2000

Amount = $12000

So, A = P(1 +r/n)^(n*t)

12000 = 10000( 1 +0.025/12)^(12*t)

12 = (1.002)^12t

taking log on both sides: ln(12) = 12tln(1.002)

t = 99.8 years