A small business has determined that the machinery they currently use will wear out in 16 years. To replace the new machine when it wears out, the company wants to establish a savings account today. If the interest rate on the account is 1.9 percent per quarter and the cost of the machinery will be $325,000, how much will the company have to deposit today

The initial deposit should be of: $97,439.62

Explanation:

Giving the following information:

To replace the new machine when it wears out, the company wants to establish a savings account today. The interest rate on the account is 1.9 percent per quarter and the cost of the machinery is $325,000.

To calculate the initial investment required, we need to use a variation on the simple interest future value formula:

FV = PV * (1+i) ^n

PV = present value

Isolating PV:

PV = FV / (1+i) ^n

i = 0.019

n = 4*16 = 64

FV = 325,000

PV = 325,000 / (1.019^64) = $97,439.62