Jane Frost wants to receive yearly payments of 15000 for 10 years. How much must she deposit at her bank today at 11% intrest compounded annually? I come up it by using calculator the following 15000 +/-
Present Value = 15000((1 - 1.11^10)/.11
Present Value =
15000[(1 - 1.11^(-10))]/.11
To calculate the amount Jane Frost must deposit at her bank today, we can use the present value of an ordinary annuity formula.
The formula for calculating the present value of an ordinary annuity is as follows:
PV = P * [(1 - (1 + r)^(-n)) / r]
Where:
PV = present value (amount Jane needs to deposit)
P = payment amount per period (yearly payment of $15,000)
r = interest rate per period (11% or 0.11)
n = number of periods (10 years)
Substituting these values into the formula, we get:
PV = 15000 * [(1 - (1 + 0.11)^(-10)) / 0.11]
Calculating this expression will give us the amount that Jane must deposit today. Let's calculate it step by step:
Step 1: Calculate the value inside the square brackets
(1 - (1 + 0.11)^(-10)) / 0.11 = 6.418075
Step 2: Multiply the value from step 1 by the payment amount per period
6.418075 * 15000 = 96211.125
Therefore, Jane Frost must deposit approximately $96,211.13 at her bank today in order to receive yearly payments of $15,000 for 10 years at an 11% interest rate compounded annually.
To find out how much Jane Frost needs to deposit at her bank today, we can use a formula called the present value of an annuity.
The formula for the present value of an annuity is:
PV = PMT * (1 - (1 + r)^(-n)) / r
where:
PV = present value
PMT = payment per period
r = interest rate per period
n = number of periods
In this case, Jane wants to receive yearly payments of $15,000 for 10 years, and the interest rate is 11% compounded annually.
Let's plug in the values into the formula:
PV = 15000 * (1 - (1 + 0.11)^(-10)) / 0.11
Using a calculator, we find that:
PV = 15000 * (1 - 1.783) / 0.11
PV = 15000 * (-0.783) / 0.11
PV = -7830000 / 0.11
PV = -712,909.09
Since Jane needs to deposit money into her bank account, the answer cannot be negative. Therefore, we discard the negative sign and take the absolute value of it.
So, Jane must deposit approximately $712,909.09 at her bank today at an 11% interest rate compounded annually in order to receive yearly payments of $15,000 for 10 years.