If $5,200 is invested at a rate of 8.6% compounded quarterly, how long will it take, to the nearest hundredth of a year, until the investment is worth $11,600?

t = 8.15 (to the nearest hundredth of a year

Step-by-step 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)