How long will it take $10,000 to grow to $12,000 if the investment earns interest at the rate of 4%/year compounded monthly? (Round your answer to one decimal place.)

Answer 1

General formula is

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

where r = rate of interest, n=number of compounding periods per year, t= years, P = beginning investment. A= ending Amount

12 = 10(1+.04/12)^12t, solve for t

12/10= 6/5 = (1.00333...)^12t

log_1.00333(1.2) = 12t

t =[ log_1.00333(1.2)]/12 = ln(1.2)/12ln(1.00333)=about 4.5651 years

a check on the answer is compare it to continuous compounding which is very close in value

12 =10e^.04t

12/10 = e^.04t

ln(1.2) = 0.04t

t = ln(1.2)/.04 = 4.5580 years, which is only slightly smaller than 4.5651

4.5651 years = 4 years, 6 months and about 21 days for $10,000 to grow to $12,000 at 4% compounded monthly

Or just 4.6 years if you're into rounding to one decimal place for years