Question

Your beginning salary is $70,000. You deposit 12% at the end of each year in a savings account that earns 3% interest. Your salary increases by 2% per year. What value does your savings book show after 40 years?

Please show the formulas

Answer 1

We would use future value of growing annuity to calculate amount at end of 40 years
Future value of growing annuity	Annuity amount*(((1+r)^n)-((1+g)^n))/(r-g)
r is interest rate, n is number of deposit and g is growth rate
Future value of growing annuity	(70000*12%)*(((1.03)^40)-((1.02)^40))/(0.03-0.02)
Future value of growing annuity	8400*((3.262038-2.20804)/0.01)
Future value of growing annuity	8400*(1.053998/0.01)
Future value of growing annuity	8400*105.3998
Future value of growing annuity	$885,358.43
Thus, at the end of 40 years the amount in savings account would be $885,358.43