Question

1..Your credit card charges a 19% APR compounded daily. What is the effective interest rate? (Please give at least 4 digits in your answer)

2.. Find the future value of the following cash flow

$1 in 4 years at 5%

(Round to the nearest cent and do not enter the dollar sign)

3.. You have the opportunity to receive $300 in one year. If you can earn 6% interest on your investments over the year, what is the most you should you pay for this opportunity?  

(Round to the nearest cent and do not enter the dollar sign)

Answer 1

Answer 1:- Effective interest rate per period (i),

Effective annual interest rate = (1 + (nominal rate / number of compounding periods)) ^ (number of compounding periods) - 1

i = (1+ r / m)^m − 1

= ( 1 + 19% / 365)³⁶⁵ - 1

= 0.20918982

or

20.9190%

So, Effective annual interest rate = 20.92%

Answer 2:-

​Future Value= I × (1+R)^T

where: I=Investment amount

R=Interest rate

T=Number of years​

So, Future Value = $1 × (1+0.05)⁴

= $1 × 1.21550625

= $1.21550625

So, Future Value is $1.22

Answer 3:- Present Value = Future Value / (1 + interest rate)^{No. of years}

Present Value = $300 / (1+0.06)¹

= $283.0188679

or

$283.02

So, the most that should be paid for this opportunity = $283.02