Question

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

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

Answer 1

First we need to find the future value in order to find the interest earned

The formula of the future value of compound continuously is
A=p e^rt
A future value?
P present value 10000
E constant
R interest rate 0.035
T time 10 years
A=10,000×e^(0.035×10)
A=14,190.68

Now calculate the interest earned by subtracting the present value from the future value
Interest earned=A-p
Interest earned=14,190.68−10,000
Interest earned=4,190.68

The rule of 70 states that if you divide 70 by interest rate, you will get how many years the investment will double
70/rate=time
70÷3.5=20 years

So Tom will have earned $(4190.68) in interest, and in (20) years the investment will double.

Hope it helps!