Question - Comparing Present Value of $8000 in 10 Years with $6433 Now
mathcompound interest calculationpresent value formulapresent value calculationcomparing present value
Solution:
The question asks you to find the present value of $8000 in 10 years given an interest rate of 2.2% compounded quarterly. To decide which is larger, $6433 now or $8000 in 10 years, we need to calculate the present value of the $8000 using the present value formula for compound interest.The present value formula is given by:\[ PV = \frac{FV}{(1 + \frac{r}{n})^{n \times t}} \]where:PV = present valueFV = future value ($8000)r = annual interest rate (2.2% or 0.022)n = number of times the interest is compounded per year (quarterly, so 4 times a year)t = number of years (10)Now let's calculate PV:\[ PV = \frac{8000}{(1 + \frac{0.022}{4})^{4 \times 10}} \]\[ PV = \frac{8000}{(1 + 0.0055)^{40}} \]\[ PV = \frac{8000}{(1.0055)^{40}} \]Using a calculator:\[ PV \approx \frac{8000}{(1.0055)^{40}} \approx \frac{8000}{2.48832} \approx 3215.77 \]Therefore, the present value of $8000 in 10 years at an interest rate of 2.2% compounded quarterly is approximately $3215.77.Now, comparing the present value of $8000 in 10 years ($3215.77) with $6433 now, it is clear that $6433 now is larger.Please note: The final answer has been rounded to the nearest cent as requested.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com