Question

3. (a) Mary wants to borrow $1200 for 2 years. She is given two options: 1) simple interest at 10% or ii) 8.5% compounded quarterly Which loan results in less interest due? (b) At what interest rate compounded monthly, would $1000 have to be invested to amount to $14017 in 7 years? ave to be invested to

Answer 1

Answer a.

Option 1:

Amount borrowed = $1,200
Period = 2 years
Interest rate = 10%

Interest due = Amount borrowed * Period * Interest rate
Interest due = $1,200 * 2 * 10%
Interest due = $240

Option 2:

Amount borrowed = $1,200
Period = 2 years or 8 quarters
Annual Interest rate = 8.50%
Quarterly interest rate = 2.125%

Amount repaid = Amount borrowed * (1 + Quarterly interest rate)^Period
Amount repaid = $1,200 * 1.02125^8
Amount repaid = $1,420

Interest due = $1,420 - $1,200
Interest due = $220

So, Option 2 will result in less interest due.

Answer b.

Amount invested = $10,000
Future value = $14,017
Period = 7 years or 84 months

Let monthly interest rate be i%

Amount invested * (1 + Monthly interest rate)^Period = Future value
$10,000 * (1 + i)^84 = $14,017
(1 + i)^84 = 1.4017
1 + i = 1.00403
i = 0.00403 or 0.403%

Monthly interest rate = 0.403%
Annual interest rate = 12 * 0.403%
Annual interest rate = 4.836% or 4.84%