Question

l wishes to provide herself, or her estate, with an income of $10,000 at the end of each year for 10 years. She will make a lump sum deposit when the account is established and add $3000 at the end of each year for 12 years. The income is to start at the end of the year following the year in which the last deposit was made. Compute the lump sum deposit. (All interest rates are 7 Percent Compounded annually)

Answer 1

Inputs

Deposit A Amount = 10,000

End of year deposits

N = 10 years

 

Deposit B Amount = 10,000

End of year deposits

N = 12 years

 

Interest Rate = 7%

 

Formula Used:

Future Value$=PMT×\frac{((1+r) ^ N −1)}{r}$

Future Value of Deposit A after 10 years

Future Value=10,000×((1.07)

10

−1)/0.07)

Future Value$=10,000×\frac{((1.07)^{10 }-1)}{0.07}$

Future Value=10,000×13.82

Future Value=10,000×13.82

Future Value=138,164.48

Future Value of Deposit B after 12 years

Future Value= 3,000×((1.07)

12

−1)/0.07)

Future Value$= 3,000×\frac{((1.07)^{12}-1)}{0.07}$

Future Value=3,000×17.89

Future Value=3,000×17.89

Future Value=53,665.35

Future Value of Deposit A after 12 years

Future Value after 12 years =Future Value after 10 years ×(1+Rate)

N

Future Value after 12 years =Future Value after 10 years ×$(1+Rate)^N$

Future Value after 12 years =138,164.48 ×$(1.07)^ 2$

Future Value after 12 years =138,164.48 ×(1.07)2

Future Value after 12 years =158,184.51 

Lump Sum Deposit = Future Value of Deposit A after 12 years + Future

 Value of Deposit B after 12 years

Lump Sum Deposit = Future Value of Deposit A after 12 years + Future Value of Deposit B after 12 years

Lump Sum Deposit = 158,184.51+53,665.35

Lump Sum Deposit = 158,184.51+53,665.35

Lump Sum Deposit =  211,849.87

Lump Sum Deposit =  211,849.87