More Time Value of Money Tutorials
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Short term time value of money refers to calculating
investments that span a life of 1 year or less. For these types of
financial calculations, we use simple time value of money formulas.
1) Short Term Interest Formula
Interest = Principal x rate of return x Time (over
365 days)
Example 1:
Best Company borrowed $10,000 based on a short term note payable. Note
has an 8% annual interest attached to it and is due in 30 days. Calculate
the interest payments?
Solution 1:
Interest = 10,000 x 0.08 x 30/365 = $65.75
Example 2:
A company borrowed $10,000 due in 90 days. The total interest paid out
was $241.15. What was the annual rate of interest?
Solution 2:
241.15 = 10,000 x R x 90/365
241.15 = R x 2465.75
R = 241.15 / 2465.75
R = 0.0978 -> 9.781%
2) Short Term Future Value
Formula
Future Value = PV x (1+ R x t)
Example 3:
Best Company invested $10,000 into a short-term investment. The investment
has an 8% annual interest attached to it and will be paid back in 30
days. What is the future value of this $10,000?
Solution 3: Future
Value = $10,000 x (1 + (0.08 x 30/365))
Future Value = $10,000 x (1+ 0.00657)
Future Value = $10,000 x 1.00657
Future Value = $10,065.7
3) Short Term Present Value
Formula
Present Value = Future Value /
[1+(R x t)] (notice that the present value formula is the same as the
Future Value formula, only the FV and PV variables are transposed using
algebraic manipulation).
Example 4:
Best Company earned $12,500 after investing in a short-term money market
instrument for 30 days. The rate of interest earned was 4.5% annual.
What original amount was invested in order to earn this $12,500?
Solution 4:
Present Value = 12500 / [ 1+ (0.045 x 30/365)]
Present Value = 12500 / (1 + 0.003698)
Present Value = 12500 / 1.003698
Present Value = $12,453.95
4)
Nominal & Effective Interest Rates
A nominal interest rate is a rate that does not
have the compounding interest effect included in it. On the other hand,
an effective interest rate has the compounding effect built into it.
Effective interest rates are the industry standard, used by car dealerships
when giving out car loans, banks when giving out business loans, etc.
So how do you convert between a nominal to effective
interest rate? The formula is:
Effective Rate = (1 + (i / n))n
- 1
where:
i = Nominal Interest Rate
n = # of compounding periods per year
Example 5:
The nominal rate or "stated rate" is 6% compounded semi-annually.
What is the Effective Rate?
Solution 5:
Effective Rate = (1 + (0.06 / 2))2 - 1
Effective Rate = (1 + 0.03)2 - 1
Effective Rate = 1.0609 - 1
Effective Rate = 0.0609 or 6.09%
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