Gary Kornig will be 30 years old next year and wants to retire when he
QUESTION
Gary Kornig will be 30 years old next year and wants to retire when he is 65. So far he has saved (1) $6,950 in an IRA account in which his money is earning 8.3 percent annually (2) $5,000 in a money market account in which he is earning 5.25 percent annuallyGary wants to have $1 million when he retires. Starting next year, he plans to invest the same amount of money every year until he retires in a mutual fund in which he expects to earn 9 percent annually. How much will Gary have to invest every year to achieve his savings goal?
Investment (1) Balance in IRA investment = PV = $6,950 Return on IRA account = i = 8.3% Time to retirement = n = 35 years Value of IRA at age 65 = FV(IRA) FV(IRA) = PV * (1 + i)^n = $6,950 * (1.083)^35 = $113,235.03 Investment (2) Balance in money market investment = PV = $5,000 Return on money market account = i = 5.25% Time to retirement = n = 35 years Value of money market at age 65 = FV(MMA) FV(MMA) = PV * (1 + i)^n = $5,000 * (1.0525)^35 = $29,973.93 Now, Target retirement balance = $1,000,000 Future value of¦
nt savings = $113,235.03 + $29,973.93 = $143,208.96 Amount needed to reach retirement target = FVA = $856,774.04 Annual payment needed to meet target = PMT Expected return from mutual fund = i= 9% FVA = PMT * [(1+i)^n 1 / i] PMT = FVA / [(1+i)^n 1 / i] PMT = $856,791.04 / [(1.09)^35 1 / 0.09] PMT = $856.791.04 / $215.711 PMT = $3,971.94
ANSWER:
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