Question

Mario wants to obtain $ 200,000 in three years through anticipated monthly deposits and extraordinary deposits, at the end of the first five semesters for a value equal to triple the monthly deposit. When the extraordinary deposit is made there is no monthly deposit, if the interest rate is equal to 18% capitalizable each month finds the value of monthly and extraordinary deposits

Answer 1

Anticipated Monthly Deposits imply advanced deposits or deposits made at the beginning of each time period. Further, there is an extraordinary deposit worth triple the monthly deposits is made at the end of five semesters (5 three month period or at the end of the 15th month). Interest Rate = 18% per annum or (18/12) = 1.5 % per month

Target Future Value = $ 200000 and let the monthly deposits be $ Y, Deposit Tenure = 3 years or 36 months

Therefore, Y x (1.015)^(36) + Y x (1.015)^(35) + ................+ Y x (1.015)^(2) + Y x (1.015) - Y x (1.015)^(21) + 3Y x (1.015)^(21) = 200000

47.9851Y - 1.36707Y + 4.10117 Y = 200000

Y = 200000 / 50.7192 = $ 3943.28

Monthly Deposits = Y = $ 3943.28 and Extraordinary Deposit = 3 x 3943.28 = $ 11829.83