Chapter 7.2, Problem 40PPSE

Solution

To write: The function that represents the total amount of money in the account in the first account after three years.

  $A=1.071P$

Given information:

The first bank offers an interest rate $3\%$ for the first year and $2\%$ for next two years.

The second bank offers an interest rate of $2.49\%$ for three years. Invested same amount of principal in each bank.

Formula Used:

  $A=P{\left(1+r\right)}^t$

Calculation:

Let principal be $P$ invested in each bank for three years.

First bank:

Amount after 1 year in the account.

  $\begin{array}{l}A=P{\left(1+0.03\right)}^1\\ A=1.03P\end{array}$

The amount after 1 year would be principal for next two years.

Amount After two years in the account:

  $\begin{array}{l}A=1.03P{\left(1+0.02\right)}^2\\ A=1.071P\end{array}$

Thus, the formula for the amount in account after three years is $A=1.071P$ .

To write: The function that represents the total amount of money in the account in the second account after three years.

  $A=1.077P$

Given information:

The first bank offers an interest rate $3\%$ for the first year and $2\%$ for next two years.

The second bank offers an interest rate of $2.49\%$ for three years. Invested same amount of principal in each bank.

Formula Used:

  $A=P{\left(1+r\right)}^t$

Calculation:

Let principal be $P$ invested in each bank for three years.

Second bank:

Amount after 3 years in the account.

  $\begin{array}{l}A=P{\left(1+0.0249\right)}^3\\ A=1.077P\end{array}$

Thus, the formula for the amount in account after three years is $A=1.077P$ .

To write: The function that represents the total amount of money in both accounts.

  $A=2.148P$

Given information:

The first bank offers an interest rate $3\%$ for the first year and $2\%$ for next two years.

The second bank offers an interest rate of $2.49\%$ for three years. Invested same amount of principal in each bank.

Formula Used:

  $A=P{\left(1+r\right)}^t$

Calculation:

First bank amount after 3 years is $A=1.071P$ .

Second bank amount after 3 years is $A=1.077P$ .

The total amount in both bank is:

  $\begin{array}{l}A=1.077P+1.071P\\ A=2.148P\end{array}$

Thus, the formula for the amount in account after three years in both account is $A=2.148P$ .