Explanation of the Topic...Present Value of a
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| PV= | $1,000 | FV= | $5,000 | |||||
| ..... | ||||||||
| 0 | 1 | 2 | 3 | ? | n = | ?? | ||
PV = FV x [ PV factor ]From the information we've been given, we know that the future value is $5,000, the present value is $1,000, and the annual interest rate is 8% compounded annually. Let's plug those numbers into our equation to solve for (n), the number of annual time periods:
| PV = | FV x [ PV factor for n = ?? years; i = 8% per year ] | |
| $1,000 = | $5,000 x [ PV factor for n = ?? years; i = 8% per year ] | |
| $1,000 / $5,000 = | PV factor for n = ?? years; i = 8% per year | |
| 0.20000 = | PV factor for n = ?? years; i = 8% per year | |
| 0.20000 = | PV factor for n = 21 years; i = 8% per year |
| PV= | $3,000 | FV= | $10,000 | |||||
| ..... | ||||||||
| ← 6 months → | ← 6 months → | ← 6 months → | ← 6 months → | |||||
| 0 | 1 | 2 | 3 | ? | n = | ?? | ||
PV = FV x [ PV factor ]From the information we've been given, we know that the future value is $10,000 and the present value is $3,000. The annual interest rate is 10% compounded semiannually, which we can restate as 5% per semiannual period. When we plug in the information we know, we can solve for (n), the number of semiannual periods:
| PV = | FV x [ PV factor for n = ?? semiannual periods; i = 5% per semiannual period ] | |
| $3,000 = | $10,000 x [ PV factor for n = ?? semiannual periods; i = 5% per semiannual period ] | |
| $3,000 / $10,000 = | PV factor for n = ?? semiannual periods; i = 5% per semiannual period | |
| 0.30000 = | PV factor for n = ?? semiannual periods; i = 5% per semiannual period | |
| 0.30000 = | PV factor for n = 25 semiannual periods; i = 5% semiannually |
| PV= | $75,000 | FV= | $100,000 | |||||
| ..... | ||||||||
| ← 1 month → | ← 1 month → | ← 1 month → | ← 1 month → | |||||
| 0 | 1 | 2 | 3 | ? | n = | ?? | ||
| PV = | FV x [ PV factor for n = ?? months ; i = 1% per month ] | |
| $75,000 = | $100,000 x [ PV factor for n = ?? months; i = 1% per month ] | |
| $75,000 / $100,000 = | PV factor for n = ?? months; i = 1% per month | |
| 0.75000 = | PV factor for n = ?? months; i = 1% per month | |
| 0.75000 = | PV factor for n = 29 months; i = 1% per month |
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