SOLUTION
From the question
The principal is $6500
a. The equation needed to calculate the compound interest is
[tex]A=P(1+r)^t[/tex]
Where
A = amount earned
P= principal
r= rate
t= time
b. Give:
t= 10 years
r = 3.7%
Substitute the values into the compound interest formula:
[tex]A=\$6500(1+3.7\%)^{10}[/tex]
Calculate the value of A
[tex]\begin{gathered} A=\$6500(1+0.037)^{10} \\ A=\$9347.62 \end{gathered}[/tex]
Hence the value of the account after 10 years is $9347.62
c. substitute t=20 into the formula
[tex]A=\$6500(1.037)^{20}[/tex]
Solve for A
[tex]A=\$13442.76[/tex]
Therefore the value of the account after 20 years is $13442.76
Since the account value after 20 is $13442.76 and the value earned over 10 years is $9347.62 then the extra interest earned is
[tex]\$13442.76-\$9347.62=\$4095.14[/tex]
Therefore He earned $4095.14 more in interest
