How much money must you pay into an account at the beginning of each of 30 years in order to have $10,000 at the end of the 30th year? Assume that the account pays 11% per annum, and round to the nearest $1.

Question

Quizplus · Accepted Answer

This is a annuity due problem where we need to find the present value of a series of payments made at the beginning of each year. Using the formula for annuity due,

Present Value = Payment x (1 - (1+r)^-n) / r x (1+r)

where r is the interest rate per period and n is the number of periods,

we can solve for the payment, which is the amount to be paid at the beginning of each year.

$10,000 = Payment x (1 - (1+0.11)^-30) / 0.11 x (1+0.11)
$10,000 = Payment x 12.1447
Payment = $823.11

Therefore, we need to pay $823.11 at the beginning of each year for 30 years to have $10,000 at the end of the 30th year. To round to the nearest dollar, we can look at the digits after the decimal point. If the digit after the cents place is 5 or greater, we round up. Otherwise, we round down. In this case, the digit after the cents place is 1, which is less than 5, so we round down to the nearest dollar, which is $823. Therefore, the answer is choice B, $45.

How Much Money Must You Pay into an Account at the Beginning