Time value of money calculations

Simple interest calculation

The time value of Money (TVM) application is used for compound interest calculations that involve regular payments.

n is the number of compounding periods. This quantity can be expressed in years, months, days, or any other time unit. n must be an integer.

i is the interest rate per year.

PV — the present value — is the initial cash flow or the present value of a series of future cash flows.

PMT is the period payment.

P/YR is the number of periods per year. The default value is 12.

FV — the future value — is the final cash flow or the compounded value of a series of prior cash flows.

The Cash Flow Sign Convention

When entering the PV, PMT, and FV cash flows, the quantities must be keyed into the calculator with the proper sign, + (plus) or – (minus), in accordance with The Cash Flow Sign Convention: Money received is entered or displayed as a positive value (+). Money paid out is entered or displayed as a negative value (–).

The Payment Mode

One more bit of information must be specified before you can solve a problem involving periodic payments. Such payments can be made either at the beginning of a compounding period (payments in advance, or annuities due) or at the end of the period (payments in arrears, or ordinary annuities). Calculations involving payments in advance yield different results than calculations involving payments in arrears. Regardless of whether payments are made in advance or in arrears, the number of payments must be the same as the number of compounding periods.

To specify the payment mode:

Press 'Begin' if payments are made at the beginning of the compounding periods.

Press 'End' if payments are made at the end of the compounding periods.

The begin or end mode is displayed on the status indicator.

You can also change it in the 'Edit mode' by clicking on the appropriate button.

Simple example :

Suppose you deposited $ 1,500 into an account that pays 6 % annual interest and is compounded monthly, and you subsequently deposited an additional $ 50 at the end of each month for the next 2 years. What amount would you have at the end of the second year.

You enter the number this way :

You click the 'FV' button and have the answer : $ 2 968,70.

Loan Calculations

You are buying a new house with a 15 years loan at 5 % annual nominal interest, compounded monthly. The price of the house is $ 350000.

What are your monthly payments?

You have to enter the values this way :

The payment is computed when you click on the 'Payment' button. The result is -2767.78. The negative sign indicates that the money is paid out.

What interest rate is needed to reduce your payment to $ 2500.

You key -2500 in the payment edit, click the 'I/YR' button and you have the result : 3.49 %.

If the interest is 5 %, what amount of money can you borrow to lower your payment to $ 2500?

You can have $ 316138.13

Saving calculations

You open an individual retirement account with a deposit of $ 30000. Every month, you save $ 500 on this account. It pays 4.5 % annual interest compounded monthly. How much will be in the account 10 years later?

You will save $ 122608.82

Lease Calculations

The first payment on a lease occurs at the beginning of the fist period. Thus, lease calculations use 'Begin' mode.

You want to lease a $ 25000 car for 3 years. The lease includes an option to buy the car for $ 9500 at the end of the lease. The interest rate of the lease is 5 %, compounded monthly. Calculate the monthly payment.

The monthly payment lease is $ 412.50.