Time Value of Money Calculator
Present Value = 0
Future Value = 0
Payment = 0
Interest/Year = 0
Periods = 0
Periods/Year = 12
Compounds/Year = 12
Payment Timing = 0
Amortization
Begin Period = 1
End Period = 1
Interest Paid = 0
Principal Paid = 0
Payment Paid = 0
End Balance = 0
Amortization Table =
Other
Years = 0
Total Interest = 0
Total PI = 0
30/365 Payment = 0
30/365¼ Payment = 0
Help
Also known as TVM or amortization, calculates compound interest problems where the payment is steady from period to period. Variables include present value, future value, payment, interest rate per year and periods.
Included are:
- amortizations
- annuities
- loans
- leases
- mortgages
- savings accounts
In addition to the standard 30/360 calendar used in standard TVM calculations, it also offers the option of calculating payment based on a 30/365 and 30/365.25 calendar.
Cash Inflows and Outflows
In time value of money problems, positive and negative numbers have different meanings: positive numbers are inflows of cash (cash received) while negative numbers are outflows (cash paid). See Understanding Cash Flows below for more details.
Rows
To calculate, enter the data you know then select ? button on the row you don't.
Time Value of Money
- Present Value: Current value of the annuity.
- Future Value: Future value of the annuity.
- Payment: Periodic payment for the annuity.
- Interest/Year: Interest per year as a percentage.
- Periods: Number of total periods. This number is the number of years and months times the periods per year. For example, if the loan is 4 years with 12 payments per year (monthly payments), periods should be 48 (4 x 12).
- Periods/Year: Number of payment periods per year. For example, if payments are made quarterly, periods per year should be 4.
- Compounds/Year: Number of interest compounding periods per year. Most of the time, compounding periods per year should equal payment periods per year. For example, if payments are made monthly and interest is compounded monthly, compounding periods per year and periods per year should both be 12.
- Payment Timing: Payments occur at the beginning or end of the period. Payments made at the beginning of the period are called Annuity Due. Most leases are this kind. A payment made at the end of the period is called an Ordinary Annuity. Most loans are this kind.
Amortization
- Begin Period: Starting period to calculate the amortization information.
- End Period: Ending period to calculate the amortization information.
- Interest Paid: Total interest paid over the amortization period.
- Principal Paid: Total principal paid over the amortization period.
- Payment Paid: Total payments made over the amortization period.
- End Balance: Balance at the end of the amortization period.
Amortizations always round to 2 decimal places.
Other
- Years: Number of years (Periods / Periods per Year)
- Total Interest: Total interest paid during the entire amortization period
- Total PI: Total principal and interest paid during the entire amortization period
- 30/365 Payment: Calculates the payment based on a 30 days per month/365 days per year (30/365) calendar basis. Standard TVM calculates on a 30/360 basic.
- 30/365¼ Payment: Calculates the payment based on a 30 days per month/365½ days per year (30/365½) calendar basis. Standard TVM calculates on a 30/360 basic.
Understanding Cash Flows
To further understand the cash flow model, here is an example of a timeline. Note that inflows of cash are treated as positive amounts (designated by no sign or a [+] sign) and outflows of cash as negative amounts (designated by a [–] sign).
[https://poweronecalc.s3.amazonaws.com/templates/tvm_loan.png | loan example]
In Time Value of Money problems the interval between cash flows are always the same and the payment amounts are always the same. In this example, the borrower receives an initial, Present Value (PV) amount followed by subsequent payments (PMT) made back to the lending institution, each an equal distance of time apart (say, one month). This is a typical loan or mortgage scenario.
Lease Example:
[https://poweronecalc.s3.amazonaws.com/templates/tvm_lease.png | lease example]
Investment Example [DEP=deposit, FV=future value]:
[https://poweronecalc.s3.amazonaws.com/templates/tvm_investment.png | investment example]
Balloon Payment Example:
[https://poweronecalc.s3.amazonaws.com/templates/tvm_balloon.png | balloon payment example]
Examples
Car Loan
When purchasing a new car, the auto dealer has offered a 12.5% interest rate over 36 months on a $7,500 loan. What will be the monthly payment?
- Payment Timing: End
- Present Value: 7,500
- Future Value: 0
- Interest/Year: 12.5%
- Periods: 36 [3 years * 12 periods/yr]
- Periods/Year: 12
- Compounds/Year: 12
Select ? on Payment row. The payment is -$250.90 per month. It is negative because it's a cash outflow.
Car Loan, Amortization
Continued from 'Car Loan' example, how much principal was paid in the first 12 periods?
- Beg Period: 1
- End Period: 12
The principal paid is -$2,196.29. It is negative because it's a cash outflow.
Retirement Annuity
With 35 years until retirement and $15,000 in the bank, how much would have to be put aside at the beginning of each month to reach $2.5 million if an interest rate of 10% can be expected?
- Payment Timing: Begin
- Present Value: -15,000
- Future Value: 2,500,000
- Interest/Year: 10.0%
- Periods: 420 [35 years * 12 periods/yr]
- Periods/Year: 12
- Compounds/Year: 12
Select ? on Payment row. The payment is -$525.15 per month. It is negative because it's a cash outflow.
Savings Account
With $3,000 in a savings account and 3.75% interest, how many months does it take to reach $4,000?
- Payment Timing: End
- Present Value: -3,000
- Future Value: 4,000
- Payment: 0
- Interest/Year: 3.75%
- Periods/Year: 12
- Compounds/Year: 12
Select ? on Periods row. To reach $4,000, it will take 92.2 periods (or 92.20 / 12 = 7.68 years).
Mortgage
You have decided to buy a house but you only have $900 to spend each month on a 30-year mortgage. The bank has quoted an interest rate of 8.75%. What is the maximum purchase price?
- Payment Timing: End
- Future Value: 0
- Payment: -900
- Interest/Year: 8.75%
- Periods: 360 [30 years * 12 periods/yr]
- Periods/Year: 12
- Compounds/Year: 12
Select ? on Present Value row. You can afford a home with a price of $114,401.87.
Mortgage w/Balloon Payment
Continued from 'Mortgage' example, you realize that you will only own the house for about 5 years and then sell it. How much will the balloon payment (the repayment to the bank) be?
- Periods: 60 [5 years * 12 periods/yr]
Select ? on Future Value row. The balloon payment will be $109,469.92 after five years.
Canadian Mortgages
Canadian mortgages compound interest twice per year instead of monthly. What is the monthly payment to fully amortize a 30-year, CA$80,000 Canadian mortgage if the interest rate is 12%?
- Payment Timing: End
- Present Value: 80,000
- Future Value: 0
- Interest/Year: 12.0%
- Periods: 360 [30 years * 12 periods/yr]
- Periods/Year: 12
- Compounds/Year: 2
Select ? on Payment row. The payment is -CA$805.11. It is negative because it is a cash outflow.
Bi-Weekly Mortgage Payments
A buyer is considering a $100,000 home loan with monthly payments, an annual interest rate of 9% and a term of 30 years. Instead of making monthly payments, the buyer realizes that he can build equity faster by making bi-weekly payments (every two weeks). How long will it take to pay off the loan?
Part 1: Calculate Monthly Payment
- Payment Timing: End
- Present Value: 100,000
- Future Value: 0
- Interest/Year: 9.0%
- Periods: 360 [30 years * 12 periods/yr]
- Periods/Year: 12
- Compounds/Year: 12
Select ? on Payment row. The monthly payment is -$804.62. It is negative because it is a cash outflow.
Part 2: Periods/Bi-Weekly Payments
- Payment: -402.31 (Payment / 2)
- Periods/Year: 26
Select ? on Periods row. Calculating shows periods equal to 567.4 periods (567.40 ¸ 26 = 21.82 years).
APR of Loan with Fees
The Annual Percentage Rate (APR) is the interest rate when fees are included with the mortgage amount. Because the fees increase the cost of the loan, the effective interest rate on the borrowed amount is higher. For example, a borrower is charged two points for the issuance of a mortgage (one point is equal to 1% of the mortgage amount). If the mortgage amount is $60,000 for 30 years with an interest rate of 11.5%, what is the APR?
Part 1: Calculate Monthly Payment
- Payment Timing: End
- Present Value: 60,000
- Future Value: 0
- Interest/Year: 11.5%
- Periods: 360 [30 years * 12 periods/yr]
- Periods/Year: 12
- Compounds/Year: 12
Select ? on Payment row. The payment is -$594.17. It is negative because it is a cash outflow.
Part 2: Calculate APR
- Present Value: 58,800 [$60,000 loan -2% fees]
Select ? on Interest/Year row. The APR is 11.764%.
Keywords
Present Value
Future Value
Payment
Interest/Year
Periods
Periods/Year
Compounds/Year
Payment Timing
Begin Period
End Period
Interest Paid
Principal Paid
Payment Paid
End Balance
Amortization Table
Years
Total Interest
Total PI
30/365 Payment
30/365¼ Payment
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PV
FV
PMT
N
IYR
TVM
Amortizations
PY
CY
30/365 Payment
annuities
loans
leases
mortgages
savings accounts
