Answer :
Alright! Let's go through this problem step-by-step.
### a) Calculate the interest earned each year:
Kim places £500 in a bank account that pays 3% simple interest per year.
Simple Interest Formula:
[tex]\[ I = P \times r \][/tex]
where:
- [tex]\( I \)[/tex] is the interest earned,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( r \)[/tex] is the annual interest rate.
Given Values:
- [tex]\( P = £500 \)[/tex]
- [tex]\( r = 3\% = 0.03 \)[/tex]
Substituting the values into the formula:
[tex]\[ I = 500 \times 0.03 \][/tex]
[tex]\[ I = 15 \][/tex]
Kim will earn £15 interest each year.
### b) Calculate the amount in the account after 1 year:
The total amount in the account after 1 year is the sum of the initial principal and the interest earned.
Amount After 1 Year Formula:
[tex]\[ A = P + I \][/tex]
where:
- [tex]\( A \)[/tex] is the final amount in the account,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( I \)[/tex] is the interest earned.
Using the values calculated in part (a):
[tex]\[ A = 500 + 15 \][/tex]
[tex]\[ A = 515 \][/tex]
After 1 year, Kim will have £515 in her account.
### Summary:
- a) Kim will earn £15 interest each year.
- b) Kim will have £515 in her account after 1 year.
### a) Calculate the interest earned each year:
Kim places £500 in a bank account that pays 3% simple interest per year.
Simple Interest Formula:
[tex]\[ I = P \times r \][/tex]
where:
- [tex]\( I \)[/tex] is the interest earned,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( r \)[/tex] is the annual interest rate.
Given Values:
- [tex]\( P = £500 \)[/tex]
- [tex]\( r = 3\% = 0.03 \)[/tex]
Substituting the values into the formula:
[tex]\[ I = 500 \times 0.03 \][/tex]
[tex]\[ I = 15 \][/tex]
Kim will earn £15 interest each year.
### b) Calculate the amount in the account after 1 year:
The total amount in the account after 1 year is the sum of the initial principal and the interest earned.
Amount After 1 Year Formula:
[tex]\[ A = P + I \][/tex]
where:
- [tex]\( A \)[/tex] is the final amount in the account,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( I \)[/tex] is the interest earned.
Using the values calculated in part (a):
[tex]\[ A = 500 + 15 \][/tex]
[tex]\[ A = 515 \][/tex]
After 1 year, Kim will have £515 in her account.
### Summary:
- a) Kim will earn £15 interest each year.
- b) Kim will have £515 in her account after 1 year.
