Question

# A local finance company quotes an interest rate of 16 percent on one-year loans. So, if...

A local finance company quotes an interest rate of 16 percent on one-year loans. So, if you borrow \$24,000, the interest for the year will be \$3,840. Because you must repay a total of \$27,840 in one year, the finance company requires you to pay \$27,840 / 12, or \$2,320.00, per month over the next 12 months. What interest rate would legally have to be quoted? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

EMI = Loan AMount / PVAF ( r%, n)

Where r is int rate per month & n is no. of months

EMI = Loan AMount / PVAF ( r%, n)

EMI = \$ 24,000 / PVAF ( r%, 12)

\$ 2320 = \$ 24,000 / PVAF ( r%, 12)

PVAF ( r%, 12) = \$24,000 / 2320

= 10.3448

or the rate at which PV of Cash Inflows are equal to PV of Cash Outflows.

The rate at which PVAF for 12 periods is 10.3448 is the rate we want.

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV for 0.5% inc ] * 0.5%

= 2% + [ 534.79 / 736.78 ] * 0.5%

= 2% + [0.73 * 0.5%]

= 2% +0.365%

= 2.365%

i,e tha Annual Int rate charged is 2.365% * 12

= 28.38% per anum

Proof :

Loan Amortization: