Concept
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Example 1
A Bank has advertised that they will lend you $200,000 for up to 2 years at a simple annual interest rate or APR of 10% with interest compounded monthly. If you borrow $200,000 for 2 years, how much you have to pay total in 2 years?
FV = 200,000 (1+.10/12)^2*12 = $244,078.19
Example 2
A Bank has advertised one of its loan offerings as follows: “We will lend you $200,000 for up to 3 years at simple annual interest rate orAPR of 8.5% with interest compounded monthly.” If you borrow $200,000 for 1 year, how much interest expense will you have accumulated over the first year and what is the bank’s APY? (You make no payments during the year and the interest accumulates over the year).
Annual Percentage Rate = 8.5%
Compounding Period (m) = 12
Periodic interest rate = APR/m =8.5%/12 = 0.70833% = .0070833 APY or EAR = (1 + 0.0070833)12 - 1 = 1.0883909 - 1 = 8.83909%
Total interest expense after 1 year = .0883909 x $200,000 = $17,678.18
Example 3
Philip needs to borrow $70,000 to start a business expansion project. His bank agrees to lend him the money over a 5-year term at an APR of 9.25% and will accept quarterly payments with no change in the quoted APR. Calculate the periodic payment and the total amount paid.
n=20
i/y = 9.25%/4;
PV = 70000;
PMT=4,411.15
Total interest paid under quarterly compounding =
20 *$4,411.15 -$70,000 = $88,223 - $70,000 = $18,223