Money can be invested at 8% annual interest compounded quarterly. Which is financially larger: receiving $2500 now, or receiving $3800 in 5 years? Compute the present value of $3800 to justify your answer.

Introduction / Context:
This question compares a lump sum available now with a larger amount to be received in the future, when money can earn compound interest. The key idea is the time value of money: a rupee or dollar today is worth more than the same amount in the future because it can earn interest. We use present value to compare the two options on an equal basis today.

Given Data / Assumptions:

• Option 1: $2500 received now (today)
• Option 2: $3800 received after 5 years
• Nominal annual interest rate r = 8%
• Compounding quarterly, so 4 periods per year
• We must find the present value of $3800 and decide which amount is larger today

Concept / Approach:
The present value PV of a future amount A under nominal rate r compounded quarterly is:
PV = A / (1 + r / 4)^(4 * T)Here T is time in years. If the present value of $3800 is greater than $2500, the future payment is more attractive at this interest rate. Otherwise, taking $2500 now would be better.

Step-by-Step Solution:
Step 1: Determine periodic rate and periods.r = 8% per annum, so rate per quarter i = 0.08 / 4 = 0.02Number of quarters in 5 years = 4 * 5 = 20Step 2: Compute present value of $3800.PV = 3800 / (1.02)^20(1.02)^20 ≈ 1.4859PV ≈ 3800 / 1.4859 ≈ $2557.29Step 3: Compare with $2500.Since $2557.29 > $2500, the $3800 in 5 years has a higher present value.

Verification / Alternative check:
We can also compute the future value of $2500 after 5 years at the same rate: FV = 2500 * (1.02)^20 ≈ 2500 * 1.4859 ≈ $3714.87, which is less than $3800. This again shows that the $3800 received in 5 years is financially better than $2500 now under 8% quarterly compounding.

Why Other Options Are Wrong:
$1557.29: Far too low, as if a much higher discount rate were used.$2567.00 and $2457.00: Close but not equal to the correctly computed present value, indicating rounding or formula errors.$2500.00: This is simply the immediate amount and not the present value of $3800.

Common Pitfalls:
Students often confuse present value and future value or forget that quarterly compounding requires dividing the rate and multiplying the time by 4. Another error is comparing 2500 directly with 3800 without adjusting for time value. Using the correct present value formula is essential to make a fair comparison.

Final Answer:
The present value of $3800 in 5 years at 8% compounded quarterly is approximately $2557.29, which is larger than $2500 now, so the $3800 in 5 years is financially more valuable.