Question

On december 31, Beth bought a yacht for $50,000 and paid $12,000 down. She agreed to pay the balance in 12 equal annual installments that include both the principal and 6% interest on the declining balance. How big will the annual payments be?

A. On December 31, Beth bought a yacht for $50,000. She paid $12,000 down, how much does she need to borrow to purchase the yacht?

$____ Round to nearest dollar

Answer 1

Cost of Yacht = $50,000
Down Payment = $12,000

Amount Borrowed = Cost of Yacht - Down Payment
Amount Borrowed = $50,000 - $12,000
Amount Borrowed = $38,000

Annual Interest Rate = 6%
Number of Payments = 12

Let Annual Payment be $x

$38,000 = $x/1.06 + $x/1.06^2 + … + $x/1.06^11 + $x/1.06^12
$38,000 = $x * (1 - (1/1.06)^12) / 0.06
$38,000 = $x * 8.383844
$x = $4,533

Annual Payment is $4,533