Respuesta :
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 [tex]2\frac{5}{8}\%[/tex] 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;
[tex]\text{Amount}=\text{Principal}\times (1+ \text{Rate of interest})^{\text{Time}}[/tex]
Or
[tex]\text{A}=\text{P}\times (1+ \text{R})^{\text{T}}[/tex]
Now, in the question we are given P = $7,976 , R = [tex]2\frac{5}{8}\%[/tex] = [tex]\frac{21}{8} \%[/tex] and T = 42 months.
So, [tex]\text{A}=\text{P}\times (1+ \text{R})^{\text{T}}[/tex]
[tex]\text{A}=7,976\times (1+ \frac{21}{8 \times 100} )^{\frac{42}{12} }[/tex]
[tex]\text{A}=7,976\times ( \frac{821}{800} )^{\frac{42}{12} }[/tex]
A = $8733.16
Hence, the total amount of money after 42 months is $8733.16.
Now, Compound Interest is calculated as;
[tex]\text{Amount}=\text{Principal}+ \text{Compound interest}[/tex]
$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.
