Problema Solution
The rule of 72 states that if an investment earns P % interest per year, it will take approximately 72/P years for your money to double.
You invest 9500 at 1.4 % interest annually. Round all answers to 2 decimal places.
According to the rule of 72, what is the doubling time, in years, for this investment?
Use the doubling time to find a formula for V(t), the value of your investment at time t. V(t) = ?
According to the doubling time, how much will your investment be worth after 24 years?
Use the compound interest formula to find how much the investment will be worth after 24 years.
Answer provided by our tutors
you invest 9500 at 1.4% interest annually.
according to the doubling formula, it will take you 72/1.4 = 51.43 years to double your money to 19000.
formula for doubling your money would be:
d = 72/1.4 = 51.43
where d = the doubling time in years.
the formula for d is 72/i% where i% is the annual interest rate expressed as a percent.
the formula for the future value of your investment is expressed by the formula:
v(t) = a*2^(t/d) where a is the present amount of your investment and t is the amount of time of your investment in years and d is the amount of time it takes to double your investment in years.
according to this formula, if d = 51.43, and t = 51.43, and a = 9500, then:
v(51.43) = 9500 * 2^(51.43 / 51.43) = 19000
this would be correct since this is where we started from.
if t = 24, then this formula becomes:
v(24) =9500 * 2^(24 / 51.43) = $13,128.05
with annual compounding, the amount that you would have after 24 years would be 9500 * (1.014)^24 = 13,262.77