Question

Is it more profitable to receive $1000 each month for 10 years or a lump sum of $182,000 at the end of 10 years? Assume that money can earn interest monthly.

Answer 1

It is more profitable to receive the lump sum amount of $182,000 at the end of 10 years, as it has a future value of $484,300.62 compared to the future value of the monthly payments which is $152,098.54.

Step-by-step explanation:

To determine which option is more profitable, we need to compare the future value of the monthly payments to the lump sum amount using compound interest.

Let's calculate the future value of the monthly payments first:

1. Calculate the monthly interest rate: 10% divided by 12 months = 0.0083333
2. Calculate the number of months: 10 years x 12 months = 120 months
3. Use the formula for future value of an ordinary annuity: Future Value = Monthly Payment x ((1 + Monthly Interest Rate)^Number of Months - 1) / Monthly Interest Rate
4. Plugging in the values, we get: Future Value = $1000 x ((1 + 0.0083333)^120 - 1) / 0.0083333 = $152,098.54

Now let's calculate the future value of the lump sum amount:

1. Use the formula for compound interest: Future Value = Present Value x (1 + Annual Interest Rate)^Number of Years
2. Plugging in the values, we get: Future Value = $182,000 x (1 + 0.10)^10 = $484,300.62

Therefore, it is more profitable to receive the lump sum amount of $182,000 at the end of 10 years, as it has a future value of $484,300.62 compared to the future value of the monthly payments which is $152,098.54.