Question

Tom invests $10,000 in a savings account that offers 3.5 percent interest, compounded continuously.

In 10 years Tom will have earned $ in interest, and in years the investment will double. (Use the rule of 70 where required.)

Answer 1

Yeah got it:)

The rule of 70 is
70/rate=Time
70÷3.5=20 years

Hope it helps

Answer 2

Part 1:

Amount invested in savings = $10000

APR = 3.5% or 0.035

t = 10 years

As given the account is compounding continuously, so the future value of compound continuously is given by:

`A=p e^(rt)`

Putting these values in formula we get;

`A=10000* e^(0.035*10)`

A = $14,190.68

Interest earned =
`14190.68-10000=4190.68` dollars

Part 2:

The rule of 70 is used to get a rough estimate of the time, in which the investment will double. So, we divide 70 by the APR to get the years.

Time =
`70/3.5`

Time = 20 years