# How to solve annuity problems

**Finance Calculator**

Texas Instruments 83

a. Future Value of a Regular Annuity

What is the Future Value of 10 equal end of period payments of $100 each, invested at an annual interest rate of 10 percent

Compounding should remain at **P/Y = 1**. **C/Y = 1**.

Enter number of years: **N = 10**

Enter interest rate: **i = 10** (press 10 and then I/Y)

Enter payment: **PMT = -100** ((-) can be found next to then ENTER key)

Not using Present Value key: **PV = 0**

Calculate unknown: ALPHA (the green key), SOLVE (above the ENTER key) **FV**. answer is **$1,593.742**

b. Unkown: Number of years .

$1,593.74 is needed sometime in the future. How long, investing $100 per year, earning 10 percent annually, would it take to amass this amount of money?

Compounding should remain at **P/Y = 1** and **C/Y = 1**

Enter interest rate: **i = 10**

Enter payment: **PMT = 100**

Enter Future Value: **FV = -1593.74**

Not using Present Value key: **PV = 0**

Calculate unknown: ALPHA, SOLVE, **N**. answer is **9.999** (round to 10)

c. Unkown: Interest rate needed

To obtain an amount of $2000.00 ten years from now, earning 10 percent annually, what amount would have to be invested on a yearly basis?

Compounding should remain at **P/Y = 1** and **C/Y = 1**

Enter Future Value: **FV = -2000.00**

Enter Present Value: **PV = 0**

Enter number of years: **N = 10**

Enter interest rate: **i = 10**

Calculate unknown: ALPHA, SOLVE, **PMT**. answer is **$125.49**

e. Present Value of a Regular Annuity

What is the present value of a 4 year annuity, with payments of $100 earning 10 percent annually?

Compounding should remain at **P/Y**

**
**

** = 1** and **C/Y = 1**

Enter number of years: **N = 4**

Enter Interest Rate: **i = 10**

Enter Payments: **PMT = $-100**

Enter Future Value: **FV = 0**

Calculate unknown: ALPHA, SOLVE, **PV**. answer is **$316.99**

*** The previous problems all deal with a regular annuities. The next set deals with an annuity due. The difference being that with an annuity due, payments are made at the beginning of the compounding periods.

Annuities Due: Time Value of Money Problems using equal beginning of period payments.

To change the setting on the calculator from regular to annuity due:

Change the PMT from E: Pmt_End to F: P_Begin

What is the Future Value of ten equal beginning of period payments of $100 each, invested at an annual interest rate of 10 percent.

Compounding should remain at **P/Y = 1**. **C/Y = 1** .

Enter number of years: **N = 10**

Enter interest rate: **i = 10**

Enter amount of payments: **PMT = -100** ((-), which can be found next to the ENTER key.)

Enter Present Value: **PV = 0**

Calculate unknown: ALPHA, SOLVE, **FV**. answer is **$1,753.12**

b. Unknown: Number of years

$1,753.12 is needed sometime in the future. How long, investing $100 per year, earning 10 percent annually, would it take to amass this amount of money?

Compounding should remain at **P/Y = 1** and **C/Y = 1**

Enter interest rate: **i = 10**

Enter payment: **PMT = 100**

Enter Future Value: **FV = -1753.12**

Not using Present Value key: **PV = 0**

c. Unkown: Interest rate needed

To obtain an amount of $3000.00 ten years from now, earning 10 percent annually, what amount would have to be invested on a yearly basis in an annuity due form?

Source: homepages.wmich.eduCategory: Credit

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