Solution-
Clare made $160 babysitting last summer. She put the money in a saving account that pays 3% interest per year.
It is a condition of compound interest with annually compounding.
We know that,
[tex]P'=P(1+r)^n[/tex]
Where,
P' = the money she will be getting after n years,
P = the money she deposited = $160
r = annual rate of interest = 3% = 0.03
n = number of years
Money she will be getting after 1 year
[tex]\Rightarrow P'=160(1+0.03)^1=160\times 1.03=\$164.8[/tex]
This is why when she multiply 1.03 with her current amount, she gets the amount she will be getting after one year.
Money she will be getting after 2 year
Taking current balance as $164.8 as at the end of one year it will be the base amount on which interest will be calculated,
[tex]\Rightarrow P'=168.8(1+0.03)^1=168.8\times 1.03=\$169.74[/tex]
Again by multiplying 1.03 she can get the amount of money she will be getting next year.
Money she will be getting after 5 year
P' = the money she will be getting after 5 years,
P = the money she deposited = $160
r = annual rate of interest = 3% = 0.03
n = 5
Putting the values,
[tex]\Rightarrow P'=160(1+0.03)^5=160\times 1.1593=\$185.49[/tex]
She will be getting $185.49 after 5 years.
We can also do this by calculating the amount of money she will be getting at the end of each year and multiplying it with 1.03 in order to get the amount of money she will be getting the next year.
Expression for the amount of money Clare would have after 30 years if she never withdraws money from the account-
[tex]\Rightarrow P'=160(1+0.03)^30[/tex]
This is the expression for the desired condition.
