Question

Starting at the end of this year, you plan to make annual deposits of $5,000 for the next 10 years followed by deposits of $13,000 for the following 10 years. The deposits earn interest of 4.6%. What will the account balance be by the end of 33 years? Round to the nearest cent.

Answer 1

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 5000*((1-(1+ 4.6/100)^-10)/(4.6/100))

PV = 39369.78

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 13000*((1-(1+ 4.6/100)^-10)/(4.6/100))

PV = 102361.43

Future value = present value*(1+ rate)^time

102361.43 = Present value*(1+0.046)^10

Present value = 65285.92

Total PV = 65285.92+39369.78=104655.7

Future value = present value*(1+ rate)^time

Future value = 104655.7*(1+0.046)^33

Future value = 461645.36