Jane Chang is making plans for a summer vacation. She will take $1,000 with her

Question

Jane Chang is making plans for a summer vacation. She will take $1,000 with her in the form of traveler’s checks. From the newspaper, she finds that if she purchases the checks by May 31, she will not have to pay a service charge. That is, she will obtain $1,000 worth of traveler’s checks for $1,000. But if she waits to buy the checks until just before starting her summer trip, she must pay a 1% service charge. (It will cost her $1,010 for $1,000 of traveler’s checks.) Jane can obtain a 13% interest rate, compounded weekly, on her money. How many weeks after May 31 can she begin her trip and still justify buying the traveler’s checks on May 31?

Explanation / Answer

Time value of money is given as " Jane can obtain a 13% interest rate, compounded weekly, on her money."

Before May 31, she will not have to pay a service charge (1%).

Amount at 13% interest rate, compounded weekly = P ( 1 + (.13/52.14))n    Where n is number of periods (weeks)

and in the question is $1000

We are required to find the number of weeks by which the interest earned is less than $10 (1% of 1000)

In case the number of weeks is 4 then interest earned is more than $10, therefore before four weeks or upto 3 weeks after may 31 she can begin her trip and still justify buying traveler's checks on May 31.

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