Question

You plan to borrow money from your grandmother to start a new chocolate candy business. You agree to make one payment of $100,000 at the end of 6 years and negotiate an interest rate of 7%. Your grandmother has offered to reduce either the interest rate or the number of years before the $100,000. Assuming your grandmother will lend you the present value of the final payment and that you want to borrow as much as possible today, which option would you prefer?

Answer 1

future payment $100,000 in 6 years

agreed interest rate 7%

the present value of the $100,000:

PV = $100,000 / (1 + 7%)⁶ = $66,634

if your grandmother really likes you and offers to either reduce the interest rate or the number of years, you should choose a reduction in the interest rate:

PV at 6% = $100,000 / (1 + 6%)⁶ = $66,634

PV at 5% = $100,000 / (1 + 5%)⁶ = $74,622

PV at 4% = $100,000 / (1 + 4%)⁶ = $79,031

PV at 3% = $100,000 / (1 + 3%)⁶ = $83,748

PV at 2% = $100,000 / (1 + 2%)⁶ = $88,797

PV at 1% = $100,000 / (1 + 1%)⁶ = $94,205

the less the interest rate, the higher the present value of the $100,000