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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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:
4=e^(.04875t) Take the natural logarithm (base e) of both sides to get:
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.
t=(ln(8))/(.04875) or t is about 42.6552
The money will increase eightfold when t is about 42.7 years.
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