Question

Bridge to College (BTC) is a not-for-profit in the small college town of University Station which encourages undergraduates to form mentor relationships with local youth. The organization heavily relies on volunteer undergraduates, but maintains a modest staff to coordinate programming and track outcomes. Both the volunteers and the funding for BTC are scarce during the summer months. The organization decided to open a credit card account and use the credit card to cover expenses before revenues come in.

(a) If BTC accumulates $50,000 credit card debt on January 1st at 12.5% interest per year, and repays it on June 1st, how much in total are they paying back if the interests are daily compounded? On June 1st, BTC will receive enough revenues to pay off all the balance in its credit card account. (Hint: how many days are there between January 1st and June 1st? Days should be the unit of period for TVM calculation)

(b) What is BTC’s interest expense because of credit card use?

Answer 1

Amount Due on 1st January $50000

Interest Rate 12.5%

Interest rates are daily compounded so we must convert the interest into Daily compounded isterest by using e^rt(e to the power or rt)

where r=Rate of Interest

t=Time Period

No. Of days from 1st january to 1st june is =31+28+31+30+31+1

=152 Days (Assumed interest is calculated on 1st jan and 1st june)

Amount payable at 1st june =Amount Utlised X e^rt

= 50000 X e^rt

= 50000 X e^(0.125X152/365)

= 50000 X e^0.05205 e power .05205 =1.0534

= 50000 X 1.0534

= 52670 (Approximatly)

a) Amount Paying Back on 1st June is $52670

b) Interest expense is 52670-50000= $ 2670