11th Grade Q1

The present value of a simple annuity is the amount of money you would need today to make a series of regular payments in the future, assuming a specific interest rate. It tells you the current worth of those future payments, considering the time value of money.

This concept is used in loans, investments, and savings plans to calculate how much a series of payments is worth right now.

Formula for Present Value of a Simple Annuity

The formula is

Where:

• $P$ = present value of the annuity
• $R$ = regular payment amount
• $i$ = interest rate per payment period
• $n$ = total number of payments

Example:

You want to borrow money to buy a laptop. The store offers a payment plan where you pay $100 per month for 12 months. The interest rate is 12% per year, compounded monthly. How much money is the loan worth today?

Step 1: Identify the values

• $R=100$ (monthly payment),
• $i=\frac{0.12}{12}=0.01$ (monthly interest rate),
• $n=12$ (12 monthly payments).

Step 2: Substitute the values into the formula

Final Answer

The present value of the loan is approximately $1136.15. This means the store is lending you $1136.15 today, and you’ll pay it back in 12 monthly payments of $100 each.