Question

Find the required annual interest rate, to the nearest tenth of a percent, for $ 1170 to grow to $ 1708

Answer 1

Answer:

Step-by-step explanation:

The formula you need for this is

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

where A(t) is the final amount after the compounding is done, P is the initial investment, r is the interest rate in decimal form, n is the number of times per year that the money is compounded, and t is the time in years. Filling in accordingly:

$1708=1170(1+\frac{r}{4})^{(4)(6)}$

First things first. Simplify by division and then multiply the n by the t to get the exponent:

Divide 1708 by 1170 to get the equation:

$1.45982906=(1+\frac{r}{4})^{24}$

Undo the 24th power by taking the 24th root of both sides to get:

$1.015888202=1+\frac{r}{4}$ Now subtract 1 from both sides to get

$.0158882024=\frac{r}{4}$ Multiply both sides by 4 to finish it off and get that

r = .0635528 but since we want the percentage, we move the decimal 2 places to the right and round to r = 6.4% which is choice A.