A bank recently announced an “instant cash” plan for holders of its bank credit

Question

A bank recently announced an “instant cash” plan for holders of its bank credit cards. A cardholder

may receive cash from the bank up to a preset limit of $500. There is a special charge of 4% made at

the time the “instant cash” is sent to the cardholders. The debt may be repaid in monthly installments

at 1.5% interest per month. Assume you borrow $150 of “instant cash” and that an initial charge of $6 (4%) is made and added to the balance due at that time. If you decide to make a monthly payment of $10, how many months are required to repay the debt? If your answer includes a fraction of a month, round up to the next month.

Explanation / Answer

present value, pv of amount to be paid back is $156

installment, a is of $10

rate of interest,r = .015% per month

n= no of months required

pv= a/(1+r) + a/(1+r)2 + ....... a/(1+r)n

156= 10/ (1+.015) +..........10/ (1+.015)n

156= 10 ( 1- (1+.015)-n ) / .015                       because of sum of goemetric progressive series

now we need to find out n

156 * 0.015 /10 =( 1- (1+.015)-n )

.234= ( 1- (1+.015)-n )

.766 = (1+.015)-n

taling log both sides

log .766= -n log 1.015

- .1157 = -n( .0064 )

n=17.9

n=18 months

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