The value of an autograph rose 40% in the last year. it is now worth $322.00. what was it worth a year ago?

Solved

Show answers

Ответ:

kris7726

24.11.2022

Mathematics

Amount obtained in Compound interest is given by :

$\bigstar\;\;\boxed{\mathsf{Amount = Principal\bigg(1 + \dfrac{Rate\;of \;interest}{100}\bigg)^{Conversion\;periods}}}$

Note : Conversion period is the time from one interest period to the next interest period. If the interest is compounded annually then there is one conversion period in an year. If the interest is compounded semi-annually then there are two conversion periods in an year. if the interest is compounded quarterly then there are four conversion periods in an year.

Problem :

Given : $500 is invested for one year at 4% annual interest

$\implies\boxed{\begin{minipage}{4 cm}\bigstar\;\;\textsf{Principal = 500}\\\\\bigstar\;\;\textsf{Time period = 1 year}\\\\\bigstar\;\;\textsf{Rate of interest = 4\%}\end{minipage}}$

As the question mentions the term ''compounded quarterly'', there are 4 conversion periods in a year.

If the interest is compounded quarterly, then the rate of interest per conversion period (quarter) will be :

$\implies \mathsf{\left(\dfrac{1}{4} \times 4\%\right) = 1\%}$

Substituting all the values in the Amount formula of C.I, We get :

$\mathsf{\implies Amount = 500\bigg(1 + \dfrac{1}{100}\bigg)^4}$

$\mathsf{\implies Amount = 500\left(1 + 0.01\right)^4}$

$\mathsf{\implies Amount = 500\left(1.01\right)^4}$

$\mathsf{\implies Amount = 520.30}$

We know that : Interest = Amount - Principal

$:\implies$ Interest = 520.30 - 500

$:\implies$ Interest = $20.30

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice