Question

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

if interest is compounded quarterly for 6 years.
A) 6.4%
B) 1.6%
C) 3.2%
D) 7.9%

Answer 1

Explanation:

The formula you need for this is

`A(t)=P(1+(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+(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+(r)/(4))^(24)`

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

`1.015888202=1+(r)/(4)` Now subtract 1 from both sides to get

`.0158882024=(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.