Financial calculations involving compound interest include savings accounts, mortgages, pension funds, leases, and annuities.
Time Value of Money (TVM) calculations, as the name implies, make use of the notion that a dollar today will be worth more than a dollar sometime in the future. A dollar today can be invested at a certain interest rate and generate a return that the same dollar in the future cannot. This TVM principle underlies the notion of interest rates, compound interest and rates of return.
TVM transactions can be represented by using cash flow diagrams. A cash flow diagram is a time line divided into equal segments representing the compounding periods. Arrows represent the cash flows, which could be positive (upward arrows) or negative (downward arrows), depending on the point of view of the lender or borrower. The following cash flow diagram shows a loan from a borrower's point of view:
Present value (PV)
(Loan) |
|
|
|
|
|
|
|
|
| |
Money |
| Equal periods |
|
|
|
| ||||
|
|
|
|
| ||||||
received is | } |
|
|
|
| |||||
} } } } |
|
| ||||||||
a positive |
|
| ||||||||
number |
|
|
|
|
|
|
|
|
|
|
1 | 2 |
| 3 |
| 4 |
| 5 |
| (PMT) | |
|
|
|
|
| ||||||
|
|
|
|
|
|
|
|
|
| |
Money | Payment Payment Payment Payment |
| Future value | |||||||
(PMT) | (PMT) | (PMT) |
| (PMT) |
| |||||
paid out is |
|
| ||||||||
|
|
|
|
|
|
|
|
| (FV) | |
a negative |
|
|
|
|
|
|
|
|
| |
| Equal payments |
|
|
|
| |||||
number |
|
|
|
|
| |||||
On the other hand, the following cash flow diagram shows a load from the lender's point of view:
Equal payments
Loan | } |
|
PV
FV
PMT PMT PMT PMT
PMT
1 2 3 4 5
} } } } }
Equal periods
In addition, cash flow diagrams specify when payments occur relative to the compounding periods: at the beginning of each period or at the end. The Finance Solver application provides both of these payment
Using the Finance Solver |