How to Calculate the Present Value of an Annuity for Awa's Future Savings
How much should be deposited today for Awa to receive $2,500 at the end of each year for the next 10 years at 5% annually?
Do you know how to calculate the present value of an annuity for Awa's future savings?
Calculating the Present Value of an Annuity for Awa's Future Savings
When planning for Awa's future savings of $2,500 at the end of each year for the next 10 years with a 5% annual interest rate, the present value of the annuity can be calculated using the formula:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
By substituting the given values into the formula and solving the equation step by step, we can determine the amount that Awa should deposit today in order to achieve her savings goal.
First, we need to plug in the values:
PMT = $2,500 (annual payment)
r = 5% or 0.05 (annual interest rate)
n = 10 years (number of payments)
After substituting the values into the formula and simplifying the equation, we find:
PV = $2,500 * [(1 - (1 + 0.05)^(-10)) / 0.05]
Calculating further:
PV = $2,500 * [(1 - 1.628895) / 0.05]
PV = $2,500 * [(-0.628895) / 0.05]
PV = $2,500 * (-12.5779)
Therefore, Awa should deposit $31,444.75 today at a 5% annual interest rate to receive $2,500 at the end of each year for the next 10 years.
Understanding how to calculate the present value of an annuity can help in efficient financial planning for future goals and savings. If you want to learn more about this concept, you can explore additional resources on financial calculations and annuities.