Answer :
Certainly! Let's solve the problem step-by-step:
### Part A: Calculate the Interest Earned Each Year
1. Identify the principal amount (initial amount):
The principal amount [tex]\( P \)[/tex] is [tex]\( £950 \)[/tex].
2. Determine the annual interest rate:
The annual interest rate [tex]\( r \)[/tex] is [tex]\( 1.6\% \)[/tex].
3. Convert the percentage to a decimal:
[tex]\( r = 1.6\% \)[/tex] can be converted to a decimal by dividing by 100.
[tex]\[ r = \frac{1.6}{100} = 0.016 \][/tex]
4. Use the simple interest formula:
The simple interest [tex]\( I \)[/tex] per year can be calculated using the formula:
[tex]\[ I = P \times r \][/tex]
Substituting the values we have:
[tex]\[ I = 950 \times 0.016 \][/tex]
5. Calculate the interest:
[tex]\[ I = 950 \times 0.016 = 15.2 \][/tex]
So, Stephen will earn £15.20 in interest each year.
### Part B: Calculate the Total Amount in the Account After 1 Year
1. Determine the total amount after 1 year:
The total amount [tex]\( A \)[/tex] after 1 year can be calculated by adding the interest earned to the principal amount.
[tex]\[ A = P + I \][/tex]
2. Substitute the values:
[tex]\[ A = 950 + 15.2 \][/tex]
3. Calculate the total amount:
[tex]\[ A = 965.2 \][/tex]
So, after 1 year, Stephen will have £965.20 in his account.
### Summary
a) Stephen will earn £15.20 in interest each year.
b) After 1 year, he will have £965.20 in his account.
### Part A: Calculate the Interest Earned Each Year
1. Identify the principal amount (initial amount):
The principal amount [tex]\( P \)[/tex] is [tex]\( £950 \)[/tex].
2. Determine the annual interest rate:
The annual interest rate [tex]\( r \)[/tex] is [tex]\( 1.6\% \)[/tex].
3. Convert the percentage to a decimal:
[tex]\( r = 1.6\% \)[/tex] can be converted to a decimal by dividing by 100.
[tex]\[ r = \frac{1.6}{100} = 0.016 \][/tex]
4. Use the simple interest formula:
The simple interest [tex]\( I \)[/tex] per year can be calculated using the formula:
[tex]\[ I = P \times r \][/tex]
Substituting the values we have:
[tex]\[ I = 950 \times 0.016 \][/tex]
5. Calculate the interest:
[tex]\[ I = 950 \times 0.016 = 15.2 \][/tex]
So, Stephen will earn £15.20 in interest each year.
### Part B: Calculate the Total Amount in the Account After 1 Year
1. Determine the total amount after 1 year:
The total amount [tex]\( A \)[/tex] after 1 year can be calculated by adding the interest earned to the principal amount.
[tex]\[ A = P + I \][/tex]
2. Substitute the values:
[tex]\[ A = 950 + 15.2 \][/tex]
3. Calculate the total amount:
[tex]\[ A = 965.2 \][/tex]
So, after 1 year, Stephen will have £965.20 in his account.
### Summary
a) Stephen will earn £15.20 in interest each year.
b) After 1 year, he will have £965.20 in his account.
