Final answer:
The discounted value of $5000 due in 10 years and 2 months with a 2.75% interest rate compounded weekly is calculated using the present value formula for continuous compounding.
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 use the present value formula for continuous compounding. The formula is as follows:
PV = P / (1 + r/n)nt
Where:
- PV is the present value
- P is the future amount ($5000)
- r is the annual interest rate (0.0275)
- n is the number of times interest is compounded per year
- t is the time in years
Since the interest is compounded weekly, n is 52. The time t is 10 years and 2 months, which is approximately 10.167 years. Inserting these values into the formula, we proceed as follows:
PV = 5000 / (1 + 0.0275/52)52*10.167
When you calculate the above, you end up with the discounted present value of the money due in 10 years and 2 months. This is a practical application of time value of money principles in finance.