How long will it take to double your money with an interest rate of 10 percent?

Question

How long will it take to double your money with an interest rate of 10 percent? 20 percent? 40 percent?

What about tenfold increase in your money with a growth rate of 50 percent?

On the advice of your broker ten years ago, you invested in a $6 stock that is now selling for $30. At what rate has your capital grown?

Your father is about to retire. His firm has given him the option of retiring with a lump sum of $50,000 or an annuity of $8,000 for ten years. Which is worth more now, if the discount rate is (1) 6%, (2) 18%?

You are offered a $15,000 life insurance policy requiring thirty annual payments of $195 each. What is the compound value of the payments that you will have made after the policy is paid up, assuming that the discount rate is 10 percent?

Explanation / Answer

1. We have a Seven-Ten rule in finance which says that the money compounded at 10% will become double in approximately 7 years. Thus, in 7 years the money will get double if compounded at 10%. For, the remaining we need to find which is as follows:
b. i = 20%
2 = 1 x (1 + 0.2)n
On solving the equation we will ge, n = 3 years approximately

c. i = 40%
2 = 1 x (1 + 0.4)n
On solving the equation we will ge, n = 1.1 years approximately

2. As per question,
20 = 10 x (1 + 0.5)n
On solving the equation we will ge, n = 1.67 years approximately

3. For this we need to ind out CAGR(Compounded Annual growth Rate)
CAGR = (Ending Value / Beginning Value)1/n - 1 = (30 / 6)1/10 - 1 = 17.46%

4. a) Present Value of $8,000 = 8,000 x PVAF(6%, 10 years) = 8,000 x 7.360 = $58,880 > $50,000. Thus, Annuity $8,000 should be selected.

b) Present Value of $8,000 = 8,000 x PVAF(18%, 10 years) = 8,000 x 4.494 = $35,952 < $50,000. Thus, $50,000 now should be selected.

5. Compound Value of payments = 195 x CVAF(10%, 30years) = 195 x 164.494 = $32,076.33

Note: The value of PVAF and CVAF is taken from the PVAF table and CVAF table respectively.

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