How would I find the formula for these problems? Please help me.. I would really appreciate it.. thank you
Calculate the present value of the following:
$7,000 in 5 years at an annual discount rate of 6%
$7,000 in 5 years at a semiannual discount rate of 6%
$7,000 in 5 years at a quarterly discount rate of 6%
$7,000 in 6 years at an annual discount rate of 6%
Please help me... thank you
can someone please show me an easy formula for these problems?
The formula I'd use is: FV = PV(1+i)^n, where
FV = future value
PV = present value
i = interest rate per period
n = number of periods
To calculate the present value of future cash flows, you can use the formula for present value, which is:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.
Let's go through each problem step by step:
1. $7,000 in 5 years at an annual discount rate of 6%:
To find the present value, substitute the given values into the formula:
PV = $7,000 / (1 + 0.06)^5
Calculate the exponent first:
(1 + 0.06)^5 = 1.338225
Now divide $7,000 by the result:
PV = $7,000 / 1.338225
The present value is approximately $5,221.38.
2. $7,000 in 5 years at a semiannual discount rate of 6%:
In this case, the discount rate needs to be adjusted to reflect the semiannual compounding process. The periodic interest rate is half of the annual rate. Therefore, the new rate is 6% / 2 = 3%.
Proceed similar to the first problem:
PV = $7,000 / (1 + 0.03)^5
Calculate the exponent:
(1 + 0.03)^5 = 1.159274
Divide $7,000 by the result:
PV = $7,000 / 1.159274
The present value is approximately $6,046.38.
3. $7,000 in 5 years at a quarterly discount rate of 6%:
Again, the discount rate needs to be adjusted to reflect the quarterly compounding process. The periodic interest rate is one-fourth of the annual rate. Therefore, the new rate is 6% / 4 = 1.5%.
Follow the same steps as before:
PV = $7,000 / (1 + 0.015)^5
Calculate the exponent:
(1 + 0.015)^5 = 1.077032
Divide $7,000 by the result:
PV = $7,000 / 1.077032
The present value is approximately $6,496.18.
4. $7,000 in 6 years at an annual discount rate of 6%:
In this case, the only difference is the time period. Substitute the given values into the formula:
PV = $7,000 / (1 + 0.06)^6
Calculate the exponent:
(1 + 0.06)^6 = 1.418510
Divide $7,000 by the result:
PV = $7,000 / 1.418510
The present value is approximately $4,933.46.
Remember to adjust the discount rate based on the compounding frequency and use the appropriate number of compounding periods when calculating the exponent.