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Question 10.EX.4: MEETING A SAVINGS GOAL Suppose that the goal is to have $75,...

MEETING A SAVINGS GOAL

Suppose that the goal is to have $75,000 in an account by the end of four years. And suppose that interest on this account is paid at a rate of 5% per year, compounded semiannually. How much must be deposited in the account today to reach this goal?

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We are given FV = $75,000, i = 5% × 2 = 2.5% per six months, and N = 4 × 2 = 8 six-month periods. Therefore, the amount of the required deposit is:

PV = \frac{\$ 75,000}{(1+0.025)^{8} }   = $61,555.99

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