Question

Nabhitha has a collection of vintage action figures that is worth $420. If the collection appreciates at a rate of 13% per year, which equation represents the value of the collection after 6 years?
Answer
Multiple Choice Answers
V, equals, 420, left parenthesis, 1, plus, 0, point, 1, 3, right parenthesis, left parenthesis, 1, plus, 0, point, 1, 3, right parenthesis, left parenthesis, 1, plus, 0, point, 1, 3, right parenthesisV=420(1+0.13)(1+0.13)(1+0.13)
V, equals, 420, left parenthesis, 0, point, 8, 7, right parenthesis, to the power 6V=420(0.87)
^6

V, equals, 420, left parenthesis, 1, point, 1, 3, right parenthesis, to the power 6V=420(1.13)
^6

V, equals, 420, left parenthesis, 0, point, 1, 3, right parenthesis, to the power 6V=420(0.13)
^6

Answer 1

To find the value of Nabhitha's collection after 6 years with a 13% annual appreciation rate, we can use the formula for compound interest:

\[
V = P(1 + r)^t
\]

Where:
- \( V \) is the future value of the investment/collection.
- \( P \) is the principal amount (initial value), which in this case is $420.
- \( r \) is the rate of appreciation (as a decimal) per year, which is 0.13 for 13%.
- \( t \) is the number of years the investment is held, which is 6 years.

Using these values, the equation becomes:

\[
V = 420(1 + 0.13)^6
\]

Simplifying further:

\[
V = 420(1.13)^6
\]

Looking at the multiple choice answers, the correct equation that represents the value of the collection after 6 years is:

\[
V = 420(1.13)^6
\]

So the answer is:

**V=420(1.13)^6**