Complete Question:
Discount loan. Up-Front Bank uses discount loans for all its customers who want one-year loans. Currently, the bank is providing one-year discount loans at 7.9%. What is the effective annual rate on these loans? If you were required to repay $205,000 at the end of the loan for one year, how much would the bank have given you at the start of the loan? If you were required to repay $205,000 at the end of the loan for one year, how much would the bank have given you at the start of the loan? $Џ (Round to the nearest dollar.)
Answer:
Up-Front Bank
a. The effective annual rate on these loans = 8.58%
b. The amount would have given $188,805.
Explanation:
a) Data and Calculations:
Discount on loans = 7.9%
Effective annual rate on the loans = 7.9%/(100% - 7.9%)
= 7.9%/92.1%
= 0.0858
= 8.58%
b) Amount to be repaid to the bank = $205,000
Amount given after the discount is deducted = $205,000 * 0.921
= $188,805
Amount deducted as interest = $16,195 ($205,000 * 7.9%)
Check:
Effective interest rate = $16,195/$188,805 * 100 = 8.58%
c) Up-Front Bank's discount loan does not require the payment of interest or any other charges. Instead, these are deducted upfront from the face amount of the loan before it is given out. The implication is that the receiver of the loan receives less than the face value. In determining the effective interest rate, the discount amount is divided by the actual loan amount received, multiplied by 100.
