Find the amount and compound interest on 8000 for 1 year at 10 per annum compounded half yearly

Given:

Present value= ₹ 8000

Interest rate= 10 % per annum

Time=1 year and compounded half yearly

To find the amount we have the formula,

Amount (A) = P (1+(R/100)2n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 8000 (1 + (10/2)/100)2

⇒ A = 8000 (1+5/100)2

⇒ A = 8000 (1+1/20)2

⇒ A = 8000 (21/20)2

⇒ A = 20 × 441

⇒ A = ₹ 8820

∴ Compound interest = A – P

= 8820 – 8000 = ₹ 820

Calculate the amount and compound interest on Rs 8,000 for 1 year at 9% per annum compounded half yearly.

Here P = Rs 8000,   T = 1 year,    R = 9% p.a.

Interest is compounded half yearly,

∴       T = 1 year = 2 half years

         R = 9% p.a.=

∵         Amount =

                     = Rs 8000

                     = Rs.

                                          = Rs

                              CI = Rs 8736.20 - Rs 8000

                      = Rs 736.20

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Calculate the amount and compound interest on:

(a) Rs 10,800 for 3 years at 121/2 % per annum compounded annually.

(b) Rs 18,000 for 21/2 years at 10% per annum compounded annually.

(c) Rs 62,500 for 11/2 years at 8% per annum compounded half yearly

(d) Rs 8,000 for 1 year at 9% per annum compounded half yearly.

(You could use the year by year calculation using SI formula to verify.)

(e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.

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(b) Two bars of soap at Rs 35 each

(c) 5 kg of flour at Rs 15 per kg

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(Hint: Find A for 2 years with interest is compounded yearly and then find SI an the 2nd year for 4/12 tears.)

Here, we shall calculate the amount for 2 years using the CI formula. Then this amount will become the principal for next 4 months, i.e. 4/12 years.

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