Question

1. An investment of $2000 earns 5.75% interest, which is compounded quarterly. After

Answer 1

Answer:

Two years investment will bring about $3,000

Step-by-step explanation:

Kindly check the attached picture for the workings.

Answer 2

Answer:

After 7.1 years

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question:

We have to find t, for which $A(t) = 3000$ when $P = 2000, r = 0.0575, n = 4$

So

$A(t) = P(1 + \frac{r}{n})^{nt}$

$3000 = 2000(1 + \frac{0.0575}{4})^{4t}$

$(1.014375)^{4t} = \frac{3000}{2000}$

$(1.014375)^{4t} = 1.5$

$\log{(1.014375)^{4t}} = \log{1.5}$

$4t\log{1.014375} = \log{1.5}$

$t = \frac{\log{1.5}}{4\log{1.014375}}$

$t = 7.1$

After 7.1 years