A person invested $17100 at 7.3% interest compounded quarterly. Estimate the number of years for the investment to double.
A) 23 B) 33 C) 10 D) 12
since we are estimating, by the rule of 72
time = appr 72/7.3 = 9.86
so what is your estimation?
10 C
To estimate the number of years for the investment to double, we need to use the compound interest formula:
A = P (1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $17,100, the annual interest rate (r) is 7.3% (or 0.073 as a decimal), and the interest is compounded quarterly (n = 4).
We want to find the value of t when the final amount A is twice the initial investment. So we substitute A = 2P into the formula and solve for t:
2P = P (1 + r/n)^(nt)
2 = (1 + 0.073/4)^(4t)
Now, we can take the natural logarithm of both sides to solve for t:
ln(2) = ln((1 + 0.073/4)^(4t))
Using the logarithmic power rule, we can bring down the exponent:
ln(2) = 4t * ln(1 + 0.073/4)
Finally, divide both sides by 4 * ln(1 + 0.073/4) to solve for t:
t = ln(2) / (4 * ln(1 + 0.073/4))
Calculating this expression using a calculator, we get:
t ≈ 9.974
Since the question asks for an estimate, we can round up the answer to the nearest whole number.
Therefore, the estimated number of years for the investment to double is 10 years.
The correct answer is C) 10.