Peter received a six month post dated check for 100,000 (the check can only be cashed after six months) he offers it to a friend for 92,000 .His friend's money is presently earning 10% compounded monthly.If there is 20% withholding tax on interest ,which is better option for the friend?? Why?? Please show the solution
in 6 months, the 92000 will be worth
92000 * (1+.10/12)^6 = 96696.90
lop off 20% of the interest (4696.90) for taxes, he is left with 95757.02
Looks like he'll be better off waiting for the $100K in 6 mo.
To determine which option is better for the friend, we need to compare the two scenarios: pursuing the post-dated check or investing the money at a 10% compounded monthly interest rate.
Option 1: Cashing the post-dated check after six months
In this option, the friend will receive $100,000 after six months but will need to pay Peter $92,000 upfront. The friend will earn interest on the remaining $8,000 for six months.
Option 2: Investing the money at a 10% compounded monthly interest rate
In this option, the friend will invest $92,000 at an interest rate of 10% compounded monthly for six months, and the earnings will be subject to a 20% withholding tax.
Now let's calculate the earnings for both options.
Option 1:
The interest earned on the remaining $8,000 for six months can be calculated using the simple interest formula:
Interest = Principal x Rate x Time
Interest = $8,000 x (10% / 12) x 6
Option 2:
To calculate the future value of the friend's investment after six months, we can use the compound interest formula:
Future Value = Principal x (1 + Rate/12)^(n*12)
Future Value = $92,000 x (1 + 10%/12)^(6*12)
After calculating the future value, we need to account for the 20% withholding tax on the interest earned. So, the final amount the friend will receive is:
Final Amount = Future Value - (Future Value x 20%)
Now we can compare the final amounts from both options. If the final amount from Option 1 is greater than the final amount from Option 2, it would be a better option for the friend.
Let's calculate the amounts and compare them:
Option 1:
Interest = $8,000 x (10% / 12) x 6
Interest ≈ $400
Final Amount = $100,000 - $92,000 + $400
Final Amount ≈ $8,400
Option 2:
Future Value = $92,000 x (1 + 10%/12)^(6*12)
Future Value ≈ $97,424.56
Final Amount = $97,424.56 - ($97,424.56 x 20%)
Final Amount ≈ $77,939.65
Comparing the final amounts:
Final Amount from Option 1 ≈ $8,400
Final Amount from Option 2 ≈ $77,939.65
From the comparison, we see that Option 2 (investing the money at a 10% compounded monthly interest rate) is the better option for the friend, as it results in a significantly higher final amount of approximately $77,939.65.