Answer to Question #275886 in Economics of Enterprise for bbsjjs2

Question

Two sisters, Joan and Jocelyn decided to save money in funds that earns 14% compounded annually but on different ways. Joan decided to save by making an end-of-year deposit of P1,000 on the first year, P1,100 on the second year, P1,210 on the third year and so on increasing the next year’s deposit by 10% of the deposit in the preceding year until the end of the 10th year. Jocelyn decided to save by just making an equal deposit of P1,400 annually for 10 years. Who has more savings at the end of 10 years and by how much bigger compared to the other sister?

Answer 1

Future Value of an investment is summation of interest accumulated on the investment value, along with the investment sum.

Annuity is the fixed payment at an equal interval of time over a specified period.

Future Value of annuity, that grows annually @ 10%

Joan's investment grows (g) annually @10%

Interest Compounded Annually (r) is 14%

First Payment (P) is P1,000

Number of Period (n) is 10 years

Jocelyn investments, Future Value with annual deposit of P1,400 for 10 years

Therefore, at the end of 10 years the investment of Joan > Investment of Jocelyn

Future Value of Joan = P27,836.59

Future Value of Jocelyn = P27,072.21

Difference = P764.38 (round off difference 1.105)