What amount would you have to invest now at 10% compounded semi-annually in order to make withdrawals of $3,500 every half-year for eight years? The first withdrawal is to be made in six months.
A) $52,224
B) $28,000
C) $37,932
D) $36,126
E) $8,255

Question

Quizplus · Accepted Answer

The correct answer is found by calculating the present value of an annuity due to the semi-annual withdrawals and the semi-annual compounding interest. Using the formula for the present value of an annuity due, where the interest rate per period is 5% (10% annual rate compounded semi-annually), the number of periods is 16 (8 years, with withdrawals every half-year), and the payment per period is $3,500, the calculation gives the present value as approximately $37,932. This accounts for the fact that each withdrawal is discounted back to the present value at the semi-annual rate, and the first withdrawal occurs in six months, aligning with the annuity due formula.

What Amount Would You Have to Invest Now at 10