Your beginning salary is 50000 You deposit 10 at the end of

Your beginning salary is $50,000. You deposit 10% at the end of each year in a savings account that earns 6% interest. Your salary increases by 5% per year. What value does your savings book show after 40 years?

Solution

The formula for the future value of a growing annuity is F = P [ (1+r)ⁿ –(1+g)ⁿ]/(r –g) where P is the first payment, r is the rate of interest per peiod , g is the growth rate and n is the number of periods.

Here P = 10% of $ 50000 = $5000, r = 6/100 = 0.06, g = 5% = 0.05 and n = 40. Then F =                  5000[(1.06)⁴⁰- (1.05)⁴⁰]/( 0.06-0.05) = 5000[ 10.28571794 – 7.039988712]/(0.01) = 5000*3.245729228/0.01 = $ 1622864.61 ( on rounding off to the nearest cent). Thus the savings book will show a value of $ 1622864.61 after 40 years.