Question

Amit borrows rupees 25000 at 10% per annum interest compounded half-yearly is rupees 8000 at the end of every 6 months calculate the amount he has to pay at the end of 18 months in order to clear the entire loan.​

Answer 1

The amount that Amit has to pay at the end of 18 months to clear the entire loan is Rs. 11720.625

Step-by-step explanation:

Prncipal Amount P = 25000 Rs.

Rate of Interest = 10% per annum

Since interest is compounded half yearly

Therefore, rate of interest for half year r = 10/2 = 5%

18 months = 3 half year

Therefore, period  n = 3

Now, using the compound interest formula

$A=P(1+\frac{r}{100})^n$

For the first 6 months (1 period), Amit needs to pay

$=25000(1+\frac{5}{100})^1$

$=25000\times (1.05)$

$=26250$ Rs.

He paid = 8000 Rs.

Now Principal amount = 26250 - 8000 = 18250

Now in the next 6 months Amit has to pay

$=18250(1+\frac{5}{100})^1$

$=18250\times 1.05$

$=19162.5$ Rs.

Amit again paid Rs. = 8000

Thus, the new principal amount = 19162.5 - 8000 = 11162.5 Rs.

In the next 6 months Amit has to pay

$=11162.5(1+\frac{5}{100})^1$

$=11162.5\times 1.05$

$=11720.625$ Rs.

Therefore, at the end of 18 months, Amit has to pay Rs. = 11720.625

Hope this answer is helpful.

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