Given:
Matthew's bank lent him $8,000 for four years at an interest rate of 6 percent, compounded annually.
To Find:
The total amount that Matthew's bank will receive after 4 years.
Answer:
The total amount the bank will receive after 4 years is $10,099.8
Step-by-step explanation:
The principal amount 'P' lent to Matthew is $8000
The time period 't' is 4 years
The lending rate 'r' is 6%
As the interest is compounded annually, we use the Compound Interest formula to calculate the amount the bank will receive 'A' after 4 years.
The formula we use is
[tex]A=P(1+r)^t\\=8000(1+\frac{6}{100})^4\\\\=8000(\frac{106}{100})^4\\\\=8000(1.06)^4\\\\=10099.81[/tex]
Thus, the total amount the bank will receive after 4 years is $10,099.8
Answer: $10,099.80
Step-by-step explanation:
Given: The principal amount (P)= $8,000
The rate of interest (i)= 6 % = 0.06
Time = 4 years
The formula to calculate the compound amount in x years is given by :-
[tex]A=P(1+i)^x[/tex]
Then the compound amount received by Matthew after 4 years will be:_
[tex]A=8000(1+0.06)^4\\\\\Rightarrow\ A=8000(1.06)^4\\\\\Rightarrow\ A=8000(1.262476)=\$10,099.808\approx\$10,099.80[/tex]
Hence, the total amount that Matthew's bank will receive afeter 4 years =$10,099.80
