Example Question - present value calculation
Here are examples of questions we've helped users solve.
Comparing Present Value of $8000 in 10 Years with $6433 Now
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 value FV = 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.
Comparing Present Values for Financial Decision
To solve this question, we need to calculate the present value of $12,000 in 5 years and compare it to the given amount of $10,074 to decide which option is better. Given: - Future value (FV) = $12,000 - Interest rate (r) = 3.4% per year, compounded quarterly - Time (t) = 5 years First, we need to adjust the interest rate for quarterly compounding. The annual rate is 3.4%, which means the quarterly rate is 3.4% divided by 4: Quarterly interest rate = r / 4 = 3.4% / 4 = 0.85% per quarter (or 0.0085 in decimal form). The number of compounding periods (n) is the number of quarters in 5 years: n = 5 years * 4 quarters/year = 20 quarters Now we can use the present value formula for compound interest: \[ PV = \frac{FV}{(1+ i)^n} \] where PV = present value (what we're solving for) FV = future value ($12,000) i = quarterly interest rate (0.0085) n = total number of quarters (20) \[ PV = \frac{12,000}{(1 + 0.0085)^{20}} \] \[ PV = \frac{12,000}{(1.0085)^{20}} \] Now, let's calculate it: \[ PV = \frac{12,000}{(1.0085)^{20}} = \frac{12,000}{1.1890576171875} \] \[ PV = 10,095.85 \] The present value of $12,000 in 5 years at a 3.4% annual interest rate compounded quarterly is approximately $10,095.85. Comparing $10,095.85 with $10,074, we can see that $10,095.85 is larger. Therefore, it is better to take the $12,000 in 5 years.
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