Answer:
t = 8.15 ( to the nearest hundredth of a year
Explanation:
In this question, we are asked to calculate the number of years(rounded off) it will take an investment which is compounded quarterly to worth a certain amount.
To compute this, we have to use the formula for compound interest.
Mathematically the said amount A is;
A = P (1+r/n)^nt
Where P is the invested amount, r is the interest rate, n is the number of times investment is compounded per year and t is the number of years.
In this , we identify the parameters as follows;
A = $11,600 , P = $5,200, n = 4(quarterly means every 3 months) , t = ? , r = 8.6%
11,600 = 5200(1 + 0.086/4)^4t
Dividing both side by 5,200;
2 = (1+0.0215)^4t
2 =(1.0215)^4t
Taking logarithm of both sides;
Log 2 = Log (1.0215)^4t
Log 2 = 4tLog 1.0215
4t = Log 2/Log 1.0215
4t = 32.5848
t = 8.1462
t = 8.15 ( to the nearest hundredth of a year)