1. Find the future value of current $1,000 5 year from now when annual interest rate 8% is compounded annually
2. Find the present value of a future value (1,000) four years from now when annual interest rate 8% is compounded quarterly.
3.Find the present value of a four year $800 annuity when annual interest rate 8% is compounded annually.
To find the future value, present value, and annuity value using compound interest, you can use the following formulas:
Future Value (FV):
FV = PV * (1 + r)^n
Present Value (PV):
PV = FV / (1 + r)^n
Annuity Value (AV):
AV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
- PV is the present value (initial amount of money)
- FV is the future value (amount of money after a period of time)
- PMT is the periodic payment made (in the case of an annuity)
- r is the interest rate (expressed as a decimal)
- n is the number of compounding periods (years for FV and PV, equal to the number of payments for AV)
Now, let's solve the provided questions:
1. Finding the future value:
Given:
PV = $1,000
r = 8% = 0.08 (as a decimal)
n = 5 years
Using the formula:
FV = PV * (1 + r)^n
FV = $1,000 * (1 + 0.08)^5
FV = $1,000 * (1.08)^5
FV ≈ $1,469.33
Therefore, the future value of $1,000 in 5 years, with an annual interest rate of 8% compounded annually, is approximately $1,469.33.
2. Finding the present value:
Given:
FV = $1,000
r = 8% = 0.08 (as a decimal)
n = 4 years
Using the formula:
PV = FV / (1 + r)^n
PV = $1,000 / (1 + 0.08)^4
PV = $1,000 / (1.02)^4
PV ≈ $735.03
Therefore, the present value of $1,000 in 4 years, with an annual interest rate of 8% compounded quarterly, is approximately $735.03.
3. Finding the present value of an annuity:
Given:
PMT = $800 (annuity payment per year)
r = 8% = 0.08 (as a decimal)
n = 4 years
Using the formula:
AV = PMT * [(1 - (1 + r)^(-n)) / r]
AV = $800 * [(1 - (1 + 0.08)^(-4)) / 0.08]
AV ≈ $2,926.61
Therefore, the present value of a four-year $800 annuity, with an annual interest rate of 8% compounded annually, is approximately $2,926.61.
1. To find the future value of $1,000 in 5 years with an annual interest rate of 8% compounded annually, we can use the formula for compound interest:
Future Value = Present Value x (1 + Interest Rate)^Time
Plugging in the values into the formula, we get:
Future Value = $1,000 x (1 + 0.08)^5
Calculating this, we have:
Future Value = $1,469.33 (rounded to two decimal places)
Therefore, the future value of $1,000 in 5 years will be approximately $1,469.33.
2. To find the present value of a future value of $1,000 in 4 years with an annual interest rate of 8% compounded quarterly, we can use the formula for compound interest:
Present Value = Future Value / (1 + Interest Rate/Compounding)^ (Compounding x Time)
Plugging in the values into the formula, we get:
Present Value = $1,000 / (1 + 0.08/4)^ (4 x 4)
Calculating this, we have:
Present Value = $705.03 (rounded to two decimal places)
Therefore, the present value of a future value of $1,000 in 4 years with quarterly compounding at an annual interest rate of 8% will be approximately $705.03.
3. To find the present value of a four-year $800 annuity when the annual interest rate is 8% compounded annually, we can use the formula for the present value of an annuity:
Present Value = Payment x (1 - (1 + Interest Rate)^-Time) / Interest Rate
Plugging in the values into the formula, we get:
Present Value = $800 x (1 - (1 + 0.08)^-4) / 0.08
Calculating this, we have:
Present Value = $2,554.73 (rounded to two decimal places)
Therefore, the present value of a four-year $800 annuity at an interest rate of 8% compounded annually will be approximately $2,554.73.