Final answer:
To determine the present discounted value for $5000 due in 10 years and 2 months with a 2.75% interest rate compounded weekly, one must use the present value formula PV = FV / (1 + r/n)^(nt), where the variables represent future value, annual interest rate, number of compounding periods per year, and time in years respectively.
Step-by-step explanation:
To compute the discounted value of $5000 due in 10 years and 2 months, with an interest rate of 2.75% compounded weekly, we will use the formula for present value (PV) of a single future amount:
PV = FV / (1 + r/n)nt
Where:
- FV is the future value of the money, which is $5000.
- r is the annual interest rate in decimal form, so 2.75% becomes 0.0275.
- n is the number of times interest is compounded per year, which is 52 for weekly compounding.
- t is the time in years, and for 10 years and 2 months, this is approximately 10.167 (10 + 2/12 years).
Now, putting these values into the formula, we get:
PV = 5000 / (1 + 0.0275/52)52 * 10.167
Calculating the expression inside the parentheses and then raising it to the power of 52 * 10.167 will give us the present value of the $5000 to be received in the future. By calculating this, we can find out how much the $5000 is worth in today's terms.