Question

3. Harriet has been depositing money into a bank account for 15 years. For the first 5 years she put in $100 per month, for the next 5 years she puts in $200 per month and for the last five years she put in $300 per month. Interest for the whole period has been at 8% convertible semiannually. Calculate the accumulated value of the payments 1 month after the final payment.

Answer 1

Amount Deposited in Bank for first five years = $ 100

Total money deposited(0-5) = 60 × 100 = $ 6,000

Amount Deposited in Bank for next  five years = $ 200

Total money deposited(5-10) = 60 × 200= $12,000

Amount Deposited in Bank for next  five years = $ 300

Total money deposited(10-15)  = $ 300×60=18,000

Principal = Total Money (0-15)= 6,000+12,000+18,000=36,000

Rate of interest = 8% semi annually = 8%/2= 4%

Time = 15 years

Simple interest = $\frac{P\times R\times T}{100}$ where P= Principal, R =Rate, T = Time

S.I =$\frac{36,000 \times 4\times15 }{100}$ = 360 × 60=$21,600

Amount = Principal + Simple interest = 36,000+ 21,600= 57,600

Now ,Principal = 57,600, Time = 1 month =1/12 yrs, Rate = 4%

S.I = $\frac{57600\times4}{12\times100} = 192$

If Rate = 8%, then S.I = 192 ×2 = $ 384

Amount  i.e accumulated value of the payments 1 month after the final payment = 57,600+ 192 =$57,792 or 57,600+ 384=$57,984