Answer:
To calculate the present value (PV) and the future value (FV) for $1,000 due in 5 years with a 10% interest rate and semiannual compounding, we can use the formula:
PV = FV / (1 + (r/n))^(nt)
Where:
PV = Present Value
FV = Future Value
r = Annual Interest Rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Given:
FV = $1,000
r = 10% or 0.10
n = 2 (semiannual compounding)
t = 5 years
We can plug these values into the formula:
PV = $1,000 / (1 + (0.10/2))^(2*5)
PV ≈ $620.92
For the second part, to calculate the annual payments for an ordinary annuity for 10 years with a PV of $1,000 at an interest rate of 8%, we use the annuity formula:
PV = Pmt * [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value
Pmt = Payment per period
r = Interest rate per period
n = Total number of periods
Given:
PV = $1,000
r = 8% or 0.08
n = 10 years
We need to solve for Pmt:
$1,000 = Pmt * [(1 - (1 + 0.08)^-10) / 0.08]
First, calculate the expression inside the brackets:
1 - (1 + 0.08)^-10 = 1 - (1.08)^-10
≈ 1 - 0.46319
≈ 0.53681
Now, divide by the interest rate:
0.53681 / 0.08 ≈ 6.7101
Now, solve for Pmt:
$1,000 = Pmt * 6.7101
Pmt ≈ $149.08
So, the annual payments for an ordinary annuity would be approximately $149.08.
To find the payments for an annuity due, the payments would remain the same; the only difference is that they would occur at the beginning of each period instead of the end. Therefore, for an annuity due, the payments would also be approximately $149.08.
Answer:
Amount due in 5 years = $1,000 Annual interest rate = 10% Semiannual interest rate = 5% Semiannual period = 10 Future value = $1,000
Explanation:
i hope this will help you.
