Sally holds an investment with an interest rate of 12.3% compounded annually.
How many years will it take for her investment to triple in value?
13
6
7
9
4
9 years
To find out how many years it will take for Sally's investment to triple in value, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the initial principal
r is the interest rate
n is the number of times interest is compounded per year
t is the time in years
In this case, let's assume Sally initially invests $1. We want to find when the value of her investment reaches $3 (triple the initial value). We can substitute these values into the formula and solve for t.
3 = 1(1 + 0.123/1)^(1t)
To solve for t, we can take the logarithm of both sides to isolate t:
log(3) = log(1 + 0.123/1)^(1t)
Using logarithmic properties, we can move the exponent to the front:
log(3) = t * log(1 + 0.123/1)
Now we can solve for t by dividing both sides by log(1 + 0.123/1):
t = log(3) / log(1 + 0.123/1)
Using a calculator, we can find that t ≈ 6.03 years. Therefore, it will take approximately 6 years for Sally's investment to triple in value.
Thus, the correct answer is 6 years.
(1 + .123)^y = 3
y = log(3) / log(1.123)