Question

Using either logarithms or a graphing​ calculator, find the time required for the initial amount to be at least equal to the final amount. $6100, deposited at 4.8% compounded monthly, to reach at least $7400.

Answer 1

i = interest rate per month = 4.8% / 12 =  0.004

n = number of months

Hence, FV = PV x (1 + i)ⁿ

Or, 7,400 = 6,100 x (1 + 0.004)ⁿ

Hence, 1.004ⁿ = 7,400 / 6,100 =  1.213115

Hence, n x ln (1.004) = ln (1.213115)

Hence, n = ln (1.213115) / ln (1.004) = 48.3943 months = 49 months (rounded off to the next integral period) = 4 years & 1 month.

Hence, it will take 49 months or say 4 years + 1 month