Question

What is the total amount that Matthew's bank will receive after lending him $8,000 for four years at an interest rate of 6 percent, compounded annually? total amount = P (1 + i)t $9,358.87 $10,099.80 $10,210.25

Answer 1

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

$A=P(1+r)^t\\=8000(1+\frac{6}{100})^4\\\\=8000(\frac{106}{100})^4\\\\=8000(1.06)^4\\\\=10099.81$

Thus, the total amount the bank will receive after 4 years is $10,099.8

Answer 2

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 :-

$A=P(1+i)^x$

Then the compound amount received by Matthew after 4 years will be:_

$A=8000(1+0.06)^4\\\\\Rightarrow\ A=8000(1.06)^4\\\\\Rightarrow\ A=8000(1.262476)=\ 10,099.808\approx\ 10,099.80$

Hence, the total amount that Matthew's bank will receive afeter 4 years =$10,099.80