Sally won $250,000 in a lottery. She bought a new car for $42,000 and new clothes for $650. She invested the rest at 4.9% per annum, compounded biweekly and withdrew an equal amount of money every 2 weeks as spending money. These withdrawals were made for 5 years. The amount of each withdrawal has to be determined.
She won $250,000 and spent $42,000 on a car and $650 on clothes; the remaining amount invested was $207,350.
Let the amount withdrawn by her biweekly be P. The interest rate is 4.9% per annum. The applicable interest rate for 2 weeks is `0.049/26` .
The present value of all the withdrawals for the next 5 years is equal to $207,350. The following formula can be used to determine the value of each withdrawal. Here it has been assumed that the withdrawals are done at the end of every 2 weeks.
The present value of all the future withdrawals is given by the following formula: `PV = (P/i)(1 - 1/(1+i)^n)`
The value of PV is 207,350. P has to be determined, with i = 0.049/26 and n = 26*5 = 130.
`207,350 = (P/(0.049/26)(1 - 1/(1+0.049/26)^130)`
`=> 207,350*(0.049/26)/(1 - 1/(1+0.049/26)^130) = P`
This gives P = 1,799.8.
The amount Sally can withdraw from the remaining $207,350 as equal amounts for the next 5 years is equal to $1,799.8.