Final answer:
To calculate how many years it will take for a sum to double at a certain interest rate with annual compounding, you can use the rule of 72. If the interest rate is 6%, it will take about 12 years; for 9%, about 8 years; for 19%, approximately 3.79 years; and for 100%, it will double in 1 year.
Step-by-step explanation:
To find out how long it will take for a lump sum to double with compound interest, we can use the rule of 72, which is a simple way to estimate the number of years required to double the invested money at a given annual rate of return. The rule states that you divide the number 72 by the interest rate to get the approximate number of years it will take for the initial investment to double.
- a. For 6%: Years = 72 / 6 = 12 years.
- b. For 9%: Years = 72 / 9 = 8 years.
- c. For 19%: Years = 72 / 19 = 3.79 years, rounded to two decimal places.
- d. For 100%: If the rate of interest is 100%, the money would double in 1 year.
The formula used is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per unit t, and t is the time the money is invested for. When the interest is compounded once a year, n is 1. However, this method provides an approximation and for precise calculation, the formula for compound interest would be used to solve for the period (t).