Question

ABC Corp. wants to save $1,000,000 to buy some new equipment four years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn an APR of 5.75 percent compounded monthly on its savings. How much does the firm have to save each quarter to achieve its goal

Answer 1

In order to achieve its goal, the amount the firm should save each quarter is $56,033.97

The formula that can be used to determine the amount that the company should save every month to achieve its goal is :

Amount = future value / annuity factor

Annuity factor = $\frac{(1 + r)^{n} - 1 }{r}$

• Future value = amount it wants to save in 4 years = $1 million
• r = interest rate = 5.75% / 4 = 1.4375%
• n = number of years = 4 x 4 = 16

Annuity factor = [(1 + 0.014375)^16 - 1] / 0.014375

= 17.846317

Amount = $1,000,000 / 17.846317

= $56,033.97

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