Jany frost wants to receive yearly payments of 15000 for 10 years. How much must she deposti at her bank today at 11% intrest compounded annually? This is what i got here and i don't think it is right. Please can anyone help me out here. 15000 n= 10x1=10 i/y=11/1=11 compute pmt=897.02 and i don't think that is right HELP
The amount that must be paid (Present Value)for an annuity with a periodic payment of $15,000 to be made at the end of each year for 10 years, at an interest rate of 11% compounded annually derives from
P = R[1-(1+i)^(-n)]/i where P = the present value, R = the periodic payment, n = the number of payment periods and i = the decimal interest paid per period.
Therefore, P = 15,000[1-(1.11)^-10]/.11 = ?
thanks that helped
To calculate how much Jany must deposit in her bank today, we can use the present value of an annuity formula. The formula is:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value (amount Jany needs to deposit today)
PMT = Yearly Payment
r = Interest Rate per period
n = Number of periods (in this case, the number of years)
Let's plug in the given values into the formula:
PMT = $15,000
r = 11% = 0.11 (when expressed as a decimal)
n = 10 years
PV = 15,000 * (1 - (1 + 0.11)^(-10)) / 0.11
Now let's solve it step-by-step to find the value of PV:
1. Calculate the value inside the parentheses: (1 + 0.11)^(-10)
= (1.11)^(-10)
≈ 0.34908 (rounded to five decimal places)
2. Subtract this value from 1 to get: 1 - 0.34908 ≈ 0.65092 (rounded to five decimal places)
3. Divide the result by the interest rate: 0.65092 / 0.11 ≈ 5.91836 (rounded to five decimal places)
4. Multiply this result by the yearly payment amount: 5.91836 * 15,000 ≈ $88,775.40 (rounded to two decimal places)
Therefore, Jany must deposit approximately $88,775.40 in her bank today at an 11% interest rate compounded annually to receive yearly payments of $15,000 for the next 10 years.