# An antique jar priced at 30,000 pesos Increases its value by 10% every Year, how Much will it cost after 5 years?

Jul 17, 2018

48315.3 pesos

#### Explanation:

Equation for compound interest

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

where
A = Total amount (principal + interest)
P = Principal (start amount)
r = annual interest rate ( decimal i.e. 50% = 0.5)
n = number of times interest is compounded per year
t = number of years of compounded increase

In this case

$A = 30000 \cdot {\left(1 + \frac{0.1}{1}\right)}^{5}$

$= 30000 \cdot {\left(1.1\right)}^{5}$

$= 30000 \cdot 1.61051$

 = 48315.3

Jul 17, 2018

color(blue)("Cost of antique jar after 5 years " = 48,315.30 " pesos"

#### Explanation:

Cost of Antique jar $= P = 30 , 000$ pesos

Annual rate of increase = R = 10%3, compound interest

No. of years $= N = 5$

Cost after 5 years $= A = P \cdot {\left(1 + \left(\frac{R}{100}\right)\right)}^{N}$

$A = 30 , 000 \cdot {\left(1 + \left(\frac{10}{100}\right)\right)}^{5} = 48 , 315.30$ pesos

Jul 18, 2018

$= 43 , 923$ pesos

#### Explanation:

An increase of 10% can be shown as:

100%+10% = 110% = 110/100 = 1.1

This is therefore the common ratio. Each term is multiplied by $1.1$

The sequence starts as:

$30 , 000 , \text{ "33,000," "36,300," } \ldots .$

${T}_{n} = a {r}^{n - 1}$

${T}_{5} = 30 , 000 \times {1.1}^{4}$

$= 43 , 923$ pesos