FRL CH 5 Time Value of Money

Rule of 72

72/r%. double your money The rule of thumb has us doubling our money in 10 years; so, from the Rule of 72, we have that 7.2 percent per year was the norm

The number of periods required to attain a desired amount of money from a fixed investment amount

financial calculator: cpt n

The future (compound) value of a lump sum investment

Future value = $1 × (1 + r)t Based on our discussion, we can calculate the future value factor for 12 percent and three years as follows: (1 + r)t = 1.123 = 1.4049 Your $400 thus grows to: $400 × 1.4049 = $561.97 After seven years, you will have: $400 × 1.127 = $400 × 2.2107 = $884.27 Thus, you will more than double your money over seven years. Because you invested $400, the interest in the $884.27 future value is $884.27 − 400 = $484.27. At 12 percent, your $400 investment earns $400 × .12 = $48 in simple interest every year. Over seven years, the simple interest thus totals 7 × $48 = $336. The other $484.27 − 336 = $148.27 is from compounding.

The present value of a lump sum investment

Present value factor = 1/(1 + r)t We need to know the PV of $400 in one year at 7 percent. Proceeding as in the previous example: Present value × 1.07 = $400 We can now solve for the present value: Present value = $400 × (1/1.07) = $373.83 Thus, $373.83 is the present value. Again, this just means that investing this amount for one year at 7 percent will give you a future value of $400.

Simple vs. compound Interest

With simple interest, the interest is not reinvested, so interest is earned each period only on the original principal. Compound-Interest earned on both the initial principal and the interest reinvested from prior periods.

The interest rate (rate of return) that is implied by the value change

You are considering a one-year investment. If you put up $1,250, you will get back $1,350. What rate is this investment paying? First, in this single-period case, the answer is fairly obvious. You are getting a total of $100 in addition to your $1,250. The implicit rate on this investment is thus $100/1,250 = 8 percent. Discount Rate:The rate used to calculate the present value of future cash flows. PV = FVt/(1 + r)t