Question

solve the following questions

1. A person is planning for his retired life. He has 10 more years of service. He would like to deposit Rs. 30,000 at the end of the first year and thereafter he wishes to deposit the same amount (Rs. 30,000) with an annual decrease of Rs. 2,000 for the next 9 years with an interest rate of 18%. Find the total amount at the end of the 10th year of the above series.

2. A person invests a sum of Rs. 50,000 in a bank at a nominal interest rate of 18% for 15 years. The compounding is monthly. Find the maturity amount of the deposit after 15 years.

Answer 1

1. Given, A1 = 30,000 , G = 2,000 , n = 10 , i = 18%

Future worth = [A1 + G(A/G, i, n)] (F/A, i, n)

                     = [30,000 + 2,000(A/G, 18%, 10)] (F/A, 18%, 10)

                     = [30,000 + 2,000(3.194)] (23.521)

                     = 36,388 * 23.521

                     = $855,882.15

Thus, the total amount at the end of the 10th year of the above series is $855,882.15.

2. Here, i = 18% / 12 = 1.5% , n = 15 * 12 = 180

Future worth = P(1 + i)ⁿ

                      = 50,000(1 + 0.015)¹⁸⁰

                      = $729,218.38

Thus, the maturity amount of the deposit after 15 years is $729,218.38.