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Nate owns a big construction company, and he anticipates that he will need to replace some of his construction vehicles that will cost him $7,600,000 after 11 years
Nate owns a big construction company, and he anticipates that he will need to replace some of his construction vehicles that will cost him $7,600,000 after 11 years. In order to make sure he has the funds when the time comes, he wants to make semiannual deposits in a sinking fund that earns interest at the rate of 2.78%/year compounded semiannually. What would be the size of deposits that Rob will be making every six months?
Expert Solution
Deposit Amount calculation
Future Value = Deposit Amount * FVAF ( Half yearly rate, Number of half years )
7600,000 = Deposit Amount on 11th year + [ Deposit Amount * FVAF { ( 2.78% / 2 ), ( 11 * 2 - 1 ) } ]
7600,000 = Deposit Amount on 11th year + [ Deposit Amount * FVAF ( 1.39%, 21 ) ]
7600,000 = Deposit Amount on 11th year + [ Deposit Amount * ( 1/1.0139 + 1/1.01392 + ..... + 1/1.013921 ) ]
7600,000 = Deposit Amount [ 1 + ( 1/1.0139 + 1/1.01392 + ..... + 1/1.013921 ) ]
7600,000 = Deposit Amount [ 1 + 24.1928 ]
Deposit Amount = 7600,000 / 25.1928
Deposit Amount = $ 301,673.49 Answer
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