A small business has determined that the machinery they currently use will wear out in 17 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 1.1 percent compounded quarterly and the cost of the machinery will be $255,000, how much will the company have to deposit today

The amount to be deposited today is: $211, 562.44

Explanation:

Compound interest is interest that is reinvested to the initial amount that was loaned or deposited in a bank account. This means that the next interest will be calculated using the principal amount (initial amount deposited) plus the interest that is reinvested in the current period. Compound interest is calculated as follows:

FV =  PV/ ((1 + (i/n))^(nT)

FV = Future value

PV = Present Value

i = interest rate

n = number of times interest rate is applied per period

T = number of periods

In this question, PV is required to determine how much money we need to deposit today. Therefore, PV is made the subject of the formula as follows:

PV = FV/((1 + (i/n))^(nT)

PV = $255,000/ (1+(0.011/4))^(4*17)

     = $255000/(1.00275)^68

     =$211,562.4443

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