A man borrows Rs 18000 at 5% per annum compound interest .If he repays Rs 6000 at the end of the first year and Rs 8000
at the end of the second year; how much should he pay at the end of the 3rd year in order to clear the account?
x + 8000(1.05) + 6000(1.05)^2 = 1800(1.05)^3
...
....
x =5822.25
( For these I make a "time graph"
on a line, mark 0 (now), year 1, year 2 , and year 3
Place 18000 above the "now"
place 6000 at 1, 8000 at 2, and x at 3
"move" all monies to position 3 )
To solve this problem, we need to understand how compound interest works. Compound interest is calculated based on the principal amount, the interest rate, and the time period.
In this case, the man borrowed Rs 18000 at a compound interest rate of 5% per annum. The interest is compounded annually, which means it is added to the principal amount each year.
First, let's calculate the amount owed at the end of the first year. The man repaid Rs 6000, so the remaining amount is Rs 18000 - Rs 6000 = Rs 12000.
To calculate the interest for the second year, we need to use the formula for compound interest:
Amount = Principal * (1 + Rate/100)^Time
Plugging in the values, we have:
Rs 12000 = Principal * (1 + 5/100)^1
Simplifying this equation, we can find the Principal:
Principal = Rs 12000 / (1 + 5/100)^1
Now, we can calculate the remaining amount at the end of the second year. The man repaid Rs 8000, so the remaining amount is:
Remaining amount = Principal - Rs 8000
To find out the amount that should be paid at the end of the third year to clear the account, we need to find the remaining amount after the third year. We can use the previous steps to find the Principal for the third year and subtract the calculated principal from the remaining amount at the end of the second year.
First, let's find the Principal for the third year:
Principal = Remaining amount at the end of the second year / (1 + 5/100)^1
Finally, we can calculate the remaining amount at the end of the third year:
Remaining amount at the end of the third year = Principal - (Remaining amount at the end of the second year - Amount repaid at the end of the second year)
Substituting all the values into the equation will give us the final answer.