Question

Celeste just borrowed 47,700 dollars. She plans to repay this loan by making equal quarterly payments of 2,271.5 dollars for 27 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

As per data provided,

Loan amount                     =             $47,700.00

Quarterly EMI is                =             $ 2,271.50

Total number of Quarters EMI’s is 27. First payment is made in later of today i.e one quarter going to finish.

At, a quarterly interest the annuity factor value is 20.9993 ($47,700.00 / $2,271.50)

Trail and Error Method:

At, 1.75% quarterly interest rate the annuity factor value is 21.3717

And at, 2% quarterly interest rate the annuity factor value is 20.7069

For, 0.25% increase in quarterly interest rate the annuity factor value decrease by 0.6648 (21.3717 – 20.7069)

Then, for 0.3724 (21.3717 – 20.9993) decrease in annuity factor value what is the percentage increase in quarterly interest rate,

= (0.3724/0.6648)*0.25%

= 0.14% will increase.

Therefore, The quarterly interest rate is 1.89% (1.75% + 0.14%)