On your ninth birthday, you received $300 which you invested at 4.5 percent interest, compounded annually. your investment is now worth $756. how old are you today?
300(1+0.045)^n = 756
1.045^n = 756/300= 2.52
n = 21 year
Your age = 9+21 = 30
Answer:
30 years
Step-by-step explanation:
On your ninth birthday, you received $300 which you invested at 4.5 percent interest, compounded annually.
Principal amount is $300
rate of interest is 4.5%
your investment is now worth $756. So amount after t year is $756
We use compound interest formula
\(A=P(1+r)^t\)
A is the final amount
P is principal amount
r is the rate of interest 0.045
t is the number of years
Plug in the values in the formula
\(756=300(1+0.045)^t\)
Divide both sides by 300
\(\frac{756}{300}=1. 045^t\)
Take ln on both sides
\(ln\frac{756}{300}=t ln(1. 045)\)
Divide both sides by ln(0.045)
t= 20.99= 21 years
9 years + 21 years = 30 years
She is 30 years old now