Question

A manufacturer of prototyping equipment wants to have $3,000,000 available 10 years from now so that a new product line can be initiated. If the company plans to deposit money each year, starting 1 year from now, the equation that represents how much the company is required to deposit each year at 10% per year interest to have the $3,000,000 immediately after the last deposit is:

Answer 1

The objective is to find the equivalent amount (A) that should be deposited at the end of every interest period for n interest periods to realize a future sum (F) at the end of the nth interest period at an interest rate of i.

A = F[i/((1 + i)ⁿ – 1)]

A = F(A/F, i, n)

(A/F, i, n) = Equal payment series sinking fund factor

F = Single future amount at the end of the nth period = $3,000,000

A = Equal amount deposited at the end of each interest period

n = Number of interest periods = 10 years

i = Interest rate = 10% or 0.1 per annum

A = 3,000,000[0.1/((1 + 0.1)¹⁰ – 1)]

A = 3,000,000(A/F, 10%, 10)

A = 3,000,000[0.1/((1.1)¹⁰ – 1)]

A = 3,000,000 × 0.06275

A = $188,236.18

The annual equal amount which must be deposited for 10 years is $188,236.18