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 one 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

Answer:

annual savings = future value / [(1 + r)ⁿ - 1 ] / n

annual savings = $3,000,000 / [(1 + 0.1)¹⁰ - 1 ] / 0.1

annual deposit = $188,236.18

Explanation:

this is an ordinary annuity

future value = $3,000,000

interest rate = 10%

periods = 10

using the future value of an annuity formula, annual deposit = future value / annuity factor

FV annuity factor, 10 periods, 10% = 15.937

annual deposit = $3,000,000 / 15.937 = $188,241.20

instead of using annuity factors, you can solve this equation:

annual deposit = future value / [(1 + r)ⁿ - 1 ] / n

annual deposit = $3,000,000 / [(1 + 0.1)¹⁰ - 1 ] / 0.1

annual deposit = $188,236.18

Both answers are very similar, the difference is only 0.00267%