A woman borrows £180,000 from a bank at 10% per annum compound interest. She repays 50,000 at the end of each year. How much does she still owe at the end of 4 years?
To calculate the remaining amount owed at the end of 4 years, we need to first determine the annual interest and the amount of the loan that is repaid each year.
The annual interest rate is 10%, which means the woman has to pay 10% of the remaining loan amount as interest each year.
The loan amount is £180,000. Therefore, the annual interest is 10% of £180,000 which equals (£180,000 x 10%) = £18,000.
She repays £50,000 at the end of each year. Therefore, the remaining loan amount after the first year is (£180,000 - £50,000) = £130,000.
To determine the remaining loan amount after each subsequent year, we need to calculate the interest accrued as well.
Thus, for the second year: The remaining loan amount (£130,000) increases by £18,000 in interest and decreases by £50,000 from the annual repayment. So, the remaining loan amount after year two is (£130,000 + £18,000 - £50,000) = £98,000.
For the third year: The remaining loan amount (£98,000) increases by £18,000 in interest and decreases by £50,000 from the annual repayment. So, the remaining loan amount after year three is (£98,000 + £18,000 - £50,000) = £66,000.
For the fourth year: The remaining loan amount (£66,000) increases by £18,000 in interest and decreases by £50,000 from the annual repayment. So, the remaining loan amount after year four is (£66,000 + £18,000 - £50,000) = £34,000.
Therefore, at the end of 4 years, she still owes the bank £34,000.
To calculate how much the woman still owes at the end of 4 years, we need to calculate the remaining loan balance after each year.
First, let's break down the information given:
- The principal amount borrowed is £180,000.
- The annual interest rate is 10%, compounded annually.
- The woman repays £50,000 at the end of each year.
To calculate the remaining balance after each year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial loan amount)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount is £180,000, the annual interest rate is 10% (or 0.10 in decimal form), the loan is compounded annually (n = 1), and the time period is 4 years (t = 4).
Now, let's calculate the remaining balance after each year:
Year 1:
A1 = £180,000(1 + 0.10/1)^(1*1)
A1 = £180,000(1 + 0.10)^(1)
A1 = £180,000(1.10)
A1 = £198,000
At the end of the first year, the woman still owes £198,000.
Year 2:
Previous balance = £198,000
Repayment made = £50,000
Remaining balance after Year 2 = £198,000 - £50,000 = £148,000
Year 2 has a remaining balance of £148,000.
Year 3:
Previous balance = £148,000
Repayment made = £50,000
Remaining balance after Year 3 = £148,000 - £50,000 = £98,000
Year 3 has a remaining balance of £98,000.
Year 4:
Previous balance = £98,000
Repayment made = £50,000
Remaining balance after Year 4 = £98,000 - £50,000 = £48,000
At the end of 4 years, the woman still owes £48,000.
Therefore, the woman still owes £48,000 at the end of the 4th year.
at end of year 1: 180000 * 1.10 - 50000 = 148,000
repeat for the next 3 years.
Or, I'm sure you have a handy formula.