.. You were offered the opportunity to purchase either a simple interest note or a simple discount note with the following terms: $33,353 at 7% for 18 months. based on the effective interest rate, which would you choose
To determine which option to choose based on the effective interest rate, we need to calculate the effective interest rate for both the simple interest note and the simple discount note.
For the simple interest note, the formula to calculate the future value (FV) is:
FV = Principal (1 + (interest rate x time))
Given that the principal is $33,353, and the interest rate is 7% for 18 months, we can calculate the future value as follows:
FV = $33,353 * (1 + (0.07 * (18/12)))
FV = $33,353 * (1 + 0.105)
FV = $33,353 * 1.105
FV = $36,784.16
Therefore, the future value of the simple interest note is $36,784.16.
For the simple discount note, the formula to calculate the future value is:
FV = Principal - ((Principal x Interest Rate) x Time)
Using the same terms, we can calculate the future value of the simple discount note as follows:
FV = $33,353 - (($33,353 x 0.07) x (18/12))
FV = $33,353 - (($33,353 x 0.07) x 1.5)
FV = $33,353 - ($2,335.71 x 1.5)
FV = $33,353 - $3,503.57
FV = $29,849.43
Therefore, the future value of the simple discount note is $29,849.43.
To calculate the effective interest rate for both notes, we can use the formula:
Effective Interest Rate = (FV - Principal) / Principal
For the simple interest note:
Effective Interest Rate = ($36,784.16 - $33,353) / $33,353
Effective Interest Rate = $3,431.16 / $33,353
Effective Interest Rate ≈ 0.103 or 10.3%
For the simple discount note:
Effective Interest Rate = ($29,849.43 - $33,353) / $33,353
Effective Interest Rate = -$3,503.57 / $33,353
Effective Interest Rate ≈ -0.105 or -10.5%
In this case, based on the effective interest rates, the simple interest note with an effective interest rate of 10.3% would be the better option.