Tyler deposits $850 into an account bearing 4 `7/8%` annual interest compounded continuously. Calculate the following; round both answers to the nearest tenth of a year. a.) How long will it take...

Tyler deposits $850 into an account bearing 4 `7/8%`

annual interest compounded continuously.

Calculate the following; round both answers to the nearest tenth of a year.

a.) How long will it take his money to quadruple?

b.) How long will it take his money to octuple?

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Tyler deposits $850 into an account bearing 4.875% annual interest compounded continuously.

The formula for compound interest is A=Pe^(rt) where A is the amount after time t (t in years), P is the principal (the amount started with), r is the annual interest rate and e is a mathematical constant (Euler's constant) that is approximately 2.71828.

(a) The money has quadrupled when the amount in the account is 4(850)=$3400. Substituting A=3400, P=850, r=.04875 we can solve for t in years:

3400=850e^(.04875t)

4=e^(.04875t) Take the natural logarithm (base e) of both sides to get:

ln(4)=.04875t

t=(ln(4))/.04875 or t is approximately 28.4368

It will take about 28.4 years to quadruple.

** The rule of 72 says that an amount will double in approximately 72/m years where m is the interest rate percent. 72/4.875 is about 14.8 years.

(b) The money will octuple when the account has 8(850)=$6800 in it.

6800=850e^(.04875t)

8=e^(.04875t)

ln(8)=.04875t

t=(ln(8))/(.04875) or t is about 42.6552

The money will increase eightfold when t is about 42.7 years.

Sources:

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