Question

What is the future value at the end of year 13 of a series of deposits that starts at $6,000 in year 1 and shrinks by 7% per year for 13 years (last deposit occurs at the end of year 13)? The annual interest rate is 7% compounded annually

Answer 1

The initial amount that is deposited is $6,000. The amount is decreasing by 7% per year The interest rate is 7% per year and the time is 13 years. First calculate the present worth of the total deposits and then calculate the future worth of it. Following is the formula to calculate the present worth Here, 41 is the initial amount of deposit ($6,000) g is the geometric gradient (-7% or-0.07) is the interest rate (7% or 0.07) n is the time period (13 years) Substitute the value in above equation P-S6, 000| (1+(-0.07))13(1 + 0.07)-13 ] 0.07-(-0.07) 1-(0.3892946) (0.4149644) 0.07+0.07 $6,000 1-0.1615434 0.14 $6,000 $35,933.85 Thus, the present worth of the total deposit is S35,933.85

Following is the formula to calculate the future value Here, P is the present value (S35,933.85) is the interest rate (7% or 0.07) n is the time period (13 years) Substitute the value in above equation. F $35,933.85(1+0.07)3 -$35,933.85 (2.409845) $86,595.01 Thus, the compounded future value is S86,595