Question

2. Jose Rodriguez Gonzales has to borrow $30,000 for 5 years. The loan will be repaid in one lump sum at the end of the loan term. Which one of the following interest rates would be the best option for Jose?

a) 2.2% interest, compounded monthly   b) 2.2% interest, compounded annually c) 4.4% interest, compounded quarterly d) 4.4 interest, compounded monthly

Answer 1

Amount borrowed = $30,000

Answer a.

Annual interest rate = 2.20%
Monthly interest rate = 0.1833%

Period = 5 years or 60 months

Amount repaid = $30,000 * 1.001833^60
Amount repaid = $30,000 * 1.116143
Amount repaid = $33,484.29

Answer b.

Annual interest rate = 2.20%
Period = 5 years

Amount repaid = $30,000 * 1.022^5
Amount repaid = $30,000 * 1.114948
Amount repaid = $33,448.44

Answer c.

Annual interest rate = 4.40%
Quarterly interest rate = 1.10%

Period = 5 years or 20 quarters

Amount repaid = $30,000 * 1.011^20
Amount repaid = $30,000 * 1.244581
Amount repaid = $37,337.43

Answer d.

Annual interest rate = 4.40%
Monthly interest rate = 0.3667%

Period = 5 years or 60 months

Amount repaid = $30,000 * 1.003667^60
Amount repaid = $30,000 * 1.245600
Amount repaid = $37,368.00

So, Option B is best as amount repaid under this option is lowest.