Question

Sylvia invested $500 in an account compounded annually with an interest rate of 8%. Manuel invested $600 in an account with a compound interest rate of 7.25%. Using the rule of 72, mc012-1.jpg, who will double their money first?
Sylvia will double her money first, in approximately 9 years.
Manuel will double his money first, in approximately 10 years.
Manuel will double his money first, in approximately 9 years.
Sylvia will double her money first, in approximately 10 years.

Answer 1

Syliva
T=72÷8=9 years

Manul
T=72÷7.25=9.9=10 years

Option A

Answer 2

Answer: Sylvia will double her money first, in approximately 9 years.

Step-by-step explanation:

By the rule of 72,

An amount is doubled with a rate of interest in a certain time when the product of the annual rate and time(in years) is equal to 72,

In the Sylvia's investment,

Rate of interest = 8 %

Let the time in which the investment doubled = x years,

Thus, by the above rule,

8 x = 72

⇒ x = 9 years,

In the Manuel's investment,

The rate of interest = 7.25

Let this investment is doubled in y years,

Thus, by the above rule,

7.25 y = 72

⇒ y = 9.93103448 ≈9.93 years

Hence, Sylvia's investment takes less time to be doubled,

⇒ Option A is correct.

Note: The rule of 72 does not always give the exact answer,

That's why number of years found by rule of 72 for each case will be said approximately.