Question

A financial institution is willing to lend you $500. However, $510 is repaid at the end of 1 week. What are the nominal and effective interest rate?

Answer 1

Given, Principal amount = $500

Amount to be repaid back : $510

i=effective interest rate per payment period(here,per week)

Using the formula, amount = principal*(1+i)

$510=$500*(1+i)

i+1=$510/$500 => i= 1.02-1 ==> i=0.02 or, i = 2%per week.

Therefore effective interest rate per week = 2%.

For nominal interest rate(r)

r= 52*2% = 100%. (Since 1 year has 52 weeks).

For effective annual interest rate : (1+0.02)⁵²-1 = 1.8003 or, 180.03%