Respuesta :
ANSWER
a = 20 years, and b = 44 years
EXPLANATION
The inital amount deposited is $2500
The interest per year on the deposit is 5%
Using the interest formula
[tex]\begin{gathered} I\text{ = }\frac{PRT}{100} \\ \text{Where I = interest, P = principal , R = rate , and T = time} \end{gathered}[/tex]How many years will it take for you to double your money
Since Balance= Principal + interest
If the money double, then the balance in your account will be
2 x the initial deposit
Balance = 2 x 2500
Balance = $5000
Since Balance = $5000
Balance = Interest + principal
Interest = Balance - Principal
Interest = 5000 - 2500
Interest = $2500
For the money to double, you must have an interest of $2500
Time can be calculated as follows
[tex]\begin{gathered} I\text{ = }\frac{p\text{ x r x t}}{100} \\ 2500\text{ = }\frac{2500\text{ x 5 x t}}{100} \\ \text{Cross multiply} \\ 2500\text{ x 100 = 2500 x 5 x t} \\ 250,\text{ 000 = 12,500t} \\ \text{Divide both sides by 12,500} \\ \frac{12500t}{12500}\text{ = }\frac{250000}{12500} \\ t\text{ = 20 years} \end{gathered}[/tex]It will take you 20 years to have double of the amount in your account
PART B
How many years will it takes for your account to reach $8000
At that moment, the total balance will be $8000
Balance = interest + principal
Interest = Balance - principal
Interest = 8000 - 2500
Interest = $5500
Appyling the interest formula
[tex]\begin{gathered} I\text{ = }\frac{p\text{ x r x t}}{100} \\ 5500\text{ = }\frac{2500\text{ x 5 x t}}{100} \\ \text{Cross multiply} \\ 5500\text{ x 100 = 2500 x 5 x t} \\ 550,\text{ 000 = 12,500 x t} \\ 550,\text{ 000 = 12,500t} \\ \text{Divide both sides by 12,500} \\ \frac{12500t}{12500}\text{ = }\frac{550,\text{ 000}}{12,500} \\ t\text{ = 44 years} \end{gathered}[/tex]It will take you 44 years for your account to reach $8, 000
