Respuesta :
Cost of bicycle = $120.
Present amount you have = $75.
$75 is deposited in account.
Given expression for balance after 2 years is [tex]75(1+r)^{2}[/tex].
Total amount after 2 years should be there = $120.
So, we would put that given equation equal to 120.
[tex]\frac{75(1+r)^{2}}{75} =\frac{120}{75}[/tex]
Now, we need to solve it for r to get the ineterest rate.
r represents the rate of interest.
75 is being multiplied on left side. We always apply reverse operation to get rid. The reverse operation of multiplication is division.
So, we need to divide both sides by 75.
[tex]\frac{75(1+r)^2}{75} =\frac{120}{75}[/tex]
[tex](1+r)^{2} =1.6[/tex]
Taking square root on both sides.[tex]\sqrt{(1+r)^{2} }= \sqrt{1.6}[/tex]
[tex]1+r = 1.265[/tex]
Subtracting 1 from both sides.
[tex]1+r -1 = 1.265-1[/tex]
r= 0.265
In order to convert decimals into percentage, we need to multiply it by 100.
So, it would become 0.265 * 100 = 26.5%.
Therefore, rate of interest is approximately 26.5% per year.
