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Sagot :
We would apply the formula for calculating compound interest which is expressed as
A = P(1 + r/n)^nt
where
A is the total amount after t years
t is the number of years
is the principal or initial amount deposited
r is the interest rate
n is the number of compounding periods in a year
From the information given,
r = 12% = 12/100 = 0.12
P = 800
n = 1 because it was compounded annually which means once per year.
a) We want to find A when t = 13. We have
A = 800(1 + 0.12/1)^1 * 13
A = 800(1 + 0.12)^13
A = 800(1.12)^13
A = 3490.79
The balance after 13 years is $3490.79
b) We want to find t when A = $13,600.05
We have
13,600.05 = 800(1 + 0.12/1)^1 *t
13,600.05 = 800(1.12/1)^t
Dividing both sides of the equation by 800, we have
13,600.05/800 = 800(1.12/1)^t/800
800 cancels out on the right. We have
17.0000625 = 1.12^t
We would take the natural log of both sides of the equation. We have
ln 17.0000625 = ln 1.12^t
On the right side, we would apply the law of logarithms which is expressed as
ln k^t = t ln k
By applying this law, we have
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