Chapter 9.9, Problem 2BGP

To determine

To write functions $M(t)=S(t)+C(t)$ .

Answer to Problem 2BGP

  $M(t)=350{\left(1+\frac{2}{100}\right)}^t+2100{\left(1\right)}^t$

  $M(2)=\$2464$

Explanation of Solution

Given information:

M deposits $350 in saving account

M deposits $2100 in checking account

Interest rate of saving account is 2%, compounded annually

No interest rate for checking account

  $M(t)=S(t)+C(t)$

Formula used:

  $A(t)=P{\left(1+\frac{r}{100}\right)}^t$

  $A(t)$ amount after t years

P principle amount

r rate of interest

t time in years

Calculation:

For saving account

  $P=350$

  $r=2\%$

  $t=t$

Using formula

  $S(t)=350{\left(1+\frac{2}{100}\right)}^t$

  $S(t)$is amount in saving account after t years

For checking account

  $P=2100$

  $r=0$

  $t=t$

Using formula

  $C(t)=2100{\left(1+\frac{0}{100}\right)}^t$

On solving,

  $C(t)=2100{\left(1\right)}^t$

As given

  $M(t)=S(t)+C(t)$

Substituting value of saving and checking account in above equation

  $M(t)=350{\left(1+\frac{2}{100}\right)}^t+2100{\left(1\right)}^t$

This represent total amount after t years

  $M(2)=350{\left(1+\frac{2}{100}\right)}^2+2100{\left(1\right)}^2$

On solving,

  $M(2)=350{\left(1.02\right)}^2+2100$

Approximate answer is

  $M(2)=\$2464$