Question

Rosie's Florist borrows $300,000 to be paid off in six years. The loan payments are semiannual with the first payment due in six months, and interest is at 6%.
What is the amount of each payment?(A) $25,500.(B) $29,761.(C) $25,750.(D) $30,139.

Answer 1

Answer:

option (D) $30,139

Explanation:

Data provided in the question:

Amount borrowed = $300,000

Interest rate = 6%

Since payments are made semi-annually

Total number of payments made in 6 years = 2 × 6 = 12

Semi-annual interest rate = 6% ÷ 2 = 3% = 0.03

Now,

Amount borrowed = Each payment × $[\frac{1-(1 + r)^{-n}}{r}]$

thus,

$300,000 = Each payment × $[\frac{1-(1 + 0.03)^{-12}}{0.03}]$

$300,000 = Each payment × 9.954

or

Each payment amount = $300,000 ÷ 9.954

= $30,138.64 ≈ $30,139

hence,

The answer is option (D) $30,139