Question

You make monthly deposits of $180 into an account that pays 3% per year. How much larger would the balance be after 4 years if interest is compounded continuously compared to monthly? Express your answer in $ to the nearest $0.10.

Answer 1

The formula for calculating future value of annuity is

A = P( (1+r)ⁿ -1/r) where, P = Principal = $180, t = Time = 4 years and r = rate of interest per period = 3/12 =1/4, n = number of periods = 12

Therefore, A = 180{ (1+1/4)¹²-1)= $10080

Also rate of interest is 3% that is compounded continuosly. Therefore total compounding period = e = 2.718

Therefore, future balance will be = total compounding period * future annuity value = 2.718 * 10080 = $ 27397.44 ( nearest to $0.10).