Question

Paul deposited $7,976 into a bank account that earns 2 5/8% compound interest annually. Calculate Paul’s interest and total after 42 months.

Answer 1

Answer:

Paul’s interest and total after 42 months is $757.16 and $8,733.16 respectively.

Step-by-step explanation:

We are given that Paul deposited $7,976 into a bank account that earns $2\frac{5}{8}\%$ compound interest annually.

Let P = Principal sum of money

     R = Rate of interest p.a.

     T = Time period

     A = Amount of money

    C.I. = Compound Interest

As, we know that amount formula for compound interest is given by;

                  $\text{Amount}=\text{Principal}\times (1+ \text{Rate of interest})^{\text{Time}}$

                                            Or

                                $\text{A}=\text{P}\times (1+ \text{R})^{\text{T}}$

Now, in the question we are given P = $7,976 , R = $2\frac{5}{8}\%$  = $\frac{21}{8} \%$ and T = 42 months.

So,   $\text{A}=\text{P}\times (1+ \text{R})^{\text{T}}$  

       $\text{A}=7,976\times (1+ \frac{21}{8 \times 100} )^{\frac{42}{12} }$

       $\text{A}=7,976\times ( \frac{821}{800} )^{\frac{42}{12} }$

       A =  $8733.16

Hence, the total amount of money after 42 months is $8733.16.

Now, Compound Interest is calculated as;

         $\text{Amount}=\text{Principal}+ \text{Compound interest}$

          $8,733.16 = $7,976 + C.I.

           C.I. =  $8,733.16 - $7,976 = $757.16

Therefore, Paul’s interest and total after 42 months is $757.16 and $8,733.16 respectively.