Question

Celeste just borrowed 36,800 dollars. She plans to repay this loan by making equal quarterly payments of 2,894.03 dollars for 14 quarters. If she makes her first quarterly payment later today, then what is the quarterly interest rate on the loan? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

Answer 1

The Rate at which PV of all instalments are equal to Loan amount will be the interest rate.

Quarter CF PVF @1.5%, Disc CF PVF@2% | Disc CF 0 $2,894.03 1 $2,894.03 2 $2,894.03 3 $2,894.03 4 $2,894.03 5 $2,894.03 6 $2,894.03 7 $2,894.03 8 $2,894.03 9 $2,894.03 10 $2,894.03 11| $2,894.03 12| $2,894.03 13| $2,894.03 PV of CF 1.0000 $ 2,894.03 1.0000$ 2,894.03 26 0.9804 2,837.28 12 0.9612 2,781.65 0.9423$ 2,727.11 71 0.9238 2,673.64 0.90572,621.21 0.8880 2,569.82 0.8706 $ 2,519.43 0.8877 $ 2,569.06 0.8535 2,470.03 0.8746$ 2,531.10 0.8368 2,421.59 0.8617 $ 2,493.69 0.8203 $ 2,374.11 0.8489 $ 2,456.84 0.8043$ 2,327.56 0.8364$ 2,420.53 0.7885 $ 2,281.92 0.9852$ 2,851. 0.9707 $ 2,809. 0.9563$ 2,767.61 0.9422 $ 2,726.71 0.9283$ 2,686.41 0.9145$ 2,646.71 0.9010 $ 2,607.60 0.8240 $ 2,384.76 0.7730 $36,845.44 $36,800.00 $45.44 $35,736.56 $36,800.00 $ -1,063.44 Loan Diff

Int Rate per Quarter = Rate at which Least +ve diff + [ Diff at that rate / change in Diff ] * change in Int rate

= 1.5% + [ 45.44 / 1108.87 ] * 0.5%

= 1.5% + [ 0.04 * 0.5%]

= 1.50% + 0.02%

= 1.52% per quarter

i.e 6.08% per anum i.e 0.0608 is the answer

Pls comment, if any further assistance is required.