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On 1/1/01, Sienna Sunset, LLC provided a loan to one of its partners, Dorothy. In six years, Dorothy will have to pay Sienna Sunset $500,000. If Dorothy invests money semiannually in a savings account that pays an annual interest rate of 7.00%, how much will she need to deposit in the account every six months?

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Answer:

Semiannual deposit= $34,241.97

Explanation:

Giving the following information:

Future value (FV)= $500,000

Number of periods (n)= 6*2= 12

Interest rate= 0.07/2= 0.035

To calculate the annual deposit, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= semiannual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (500,000*0.035) / [(1.035^12) - 1]

A= $34,241.97

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