When preparing for a business trip to China, Kaylee Putbrese determined she needed to bring $5,200. How much must she borrow for a simple discount note at 6% for 45 days?

The question is confusing with regards to what exactly is being asked. it is not clear whether we should calculate the amount she must borrow now if she wants to pay $4500 in 45 days given a 6% note or How much would she pay in 45 days if she borrows $5200 today. I have provided solution for all scenarios.

Value = 4500

r = 0.06/365 = 0.00016484

n = 45 days

Let X be the the amount she must borrow now

Value = X (1 + rn)

4500 = X (1 + 0.00016484 x 45)

4500 = X (1.0074178)

X = 4500/1.0074178 = 4466.8379729

X = 4466.84.

if she wants to pay the exact $4500 she must borrow $4466.84 now

or if she wants to take $4500 she must invest $ 446.84 on a 6% note 45 days.

Future Value of 4500 in 45 days

Future Value = 4500 (1 + 0.00016484 x 45) = 45333.3801

Future Value = 45333.38

she would need to pay $45333.38 in 45 days if she takes $4500 now for her trip

Borrowed amount = $5417

Explanation:

Discount note = 4%

This means that Kaylee has 100 - 4 = 96% of the borrowed amount at hand

Cash at hand = $5,200

Let the borrowed amount = X

Cash at hand = 96% of X

5200 = (96/100) * X

X = (5200 * 100) / 96

X = $5417

Borrowed amount = $5417