Question

An investment is advertised as returning 5.5% every 6 months (semiannually), compounded semiannually. If $50,000 is invested, the growth can be modeled by the equation A(t) = 50,000(1.055)2t. What is the equivalent annual growth rate for this investment (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest ten-thousand dollar) after 20 years?

Answer 1

(A) 11.3% (B) $430,000

Step-by-step explanation:

There seems to be an error in the compounding equation written as A(t) = 50,000(1.055)2t.

Compounding the semi annual return, the equation should be

`A(t) = 50,000 * 1.055^(2t)`

where t is the number of years.

The equation is similar to the first expected that 1.055 is raised to the power of (2t) and not multiplied by it.

(A) Compounding at 5.5% semi-annually, the equivalent annual growth rate is computed as follows.

=
`1.055^(2) -1`

= 1.113025 - 1

= 0.113025 = 11.3025%

= 11.3% (to the nearest tenth of a percent).

(B) In 20 years, the investment will be worth

`A(t) = 50,000 * 1.055^(2t)` (where t=20)

=
`A(t) = 50,000 * 1.055^(2*20)`

=
`A(t) = 50,000 * 1.055^(40)`

= 50,000 * 8.5133

= $425,665

= $430,000 (to the nearest ten thousand dollars)