Question

3. A man invests ₹ 12800 at 5 % per annum compound interest for three years. Calculate: (i) The interest for the second year. (ii) The amount standing to his credit at the end of the second year. (iii) The interest for the third year​

Answer 1

Step-by-step explanation:

Given :-

A man invests ₹ 12800 at 5 % per annum compound interest for three years.

To find :-

Calculate the following :

(i) The interest for the second year?

(ii) The amount standing to his credit at the end of the second year?

(iii) The interest for the third year?

Solid :-

The money invested by a man = ₹ 12800

Rate of interest per annum = 5%

Time = 3 years

Interest is calculated compounded per annum

i) The Interest end of the first year

=> I = PTR/100

=> I = 12800×5×1/100

=> I = 128×5

=> I = ₹ 640

Now

Amount = Principle + Interest

=> A = 12800+640

=> A = ₹ 13440

So, It will be the Principle for the second year

Now

Interest for the second year

=> I = (13440×1×5)/100

=> I = 1344×5/10

=> I = 1344/2

=>I =₹ 672

Interest for the second year = ₹ 672

ii)Amount = Principle + Interest

=> A = 13440+672

=> A = ₹ 14112

The amount standing to his credit at the end of the second year = ₹ 14112

iii)The principle for the third year = ₹ 14112

=> I = (14112×5×1)/100

=> I = 14112/20

=> I = 7056/10

=> I = ₹ 705.6

or

We know that

A = P[1+(R/100)]^n

We have,

P = 12800

R = 5%

n = 3

=> A = 12800[1+(5/100)]³

=> A = 12800[1+(1/20)]³

=> A = 12800[(20+1)/20]³

=> A = 12800[21/20]3

=> A = (12800×21×21×21)/(20×20×20)

=> A =118540800/8000

=> A = 14817.6

We know that

A = P+I

=> I = A-P

=> I = 14817.6-12800

=> I = 2017.6

The Interest for three years = 2017.6

The interest for first two years =640+672

=> 1312

Interest for third year = 2017.6-1312 = 705.6

Answer:-

I) Interest for the second year = ₹ 672

ii)The amount standing to his credit at the end of the second year = ₹ 14112

iii)The interest for the third year= ₹ 705.6

Used formulae:-

• S.I= PTR/100
• A = P[1+(R/100)]^n
• A = P+I
• P = Principle
• A = Amount
• I = Interest
• R = Rate of Interest
• n = Number of times the interest is calculated compoundly.

Answer 2

$\overline{\underline{\boxed{\sf GIVEN \darr}}}$

A man invests ₹ 12800 at 5 % per annum compound interest for three years. Calculate:

(i) The interest for the second year.

(ii) The amount standing to his credit at the end of the second year.

(iii) The interest for the third year

$\overline{\underline{\boxed{\sf SOLUTION \darr}}}$

Given that :

• Principal = ₹ 12800

• Rate of Interest = 5 % p.a (per annum)

• Time = 3 years

Solution (I) :

Principal = ₹ 12800, Rate of Interest = 5, Time = 1 year

Interest for the first year = P × R × T/100

Interest = 12800 × 5 ×1/100

Interest = 12800/20

Interest = ₹ 640

Hence, Interest for 1st year is ₹ 640

Amount after 1 year = Interest + Principal

Amount = ₹ 640 + ₹ 12800

Amount = ₹ 13440

Amount after 1 year = Principal for 2nd year

2ND YEAR

Principal = ₹ 13450, Rate of Interest = 5, Time = 1 year

Interest for the first year = P × R × T/100

Interest = 13440 × 5 ×1/100

Interest = 13440/20

Interest = ₹ 672

Henceforth, Interest for the second year is ₹ 672

Solution (II) :

Amount after 2nd year = Interest + Principal

Amount = ₹ 672 + ₹ 13440

Amount = ₹ 14112

Therefore, Amount after 2 years is ₹ 14112

Solution (III) :

Principal = ₹ 14112, Rate of Interest = 5, Time = 1 year

Interest for the first year = P × R × T/100

Interest = 14112 × 5 ×1/100

Interest = 14112/20

Interest = ₹ 705.6

Hence, Interest after third year is ₹ 705.6

$\overline{\underline{\boxed{\sf KNOW \: MORE \darr}}}$

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

Used for finding the amount, principal, time and rate at complete years

$\sf \purple{A = P {(1 + \frac{r}{200}) }^{2n} }$

Used for finding amount, principal, time and rate at half years

$\sf \green{A = P {(1 + \frac{r}{400})}^{4n} }$

Used for finding amount, principal, time and rate at quarters

$\sf \blue{ A = P(1 + \frac{ r_{1}}{100} )(1 + \frac{r_{2}}{100}) }$

Used for finding rate of Interestat successive years

$\sf \pink{Compound \: Interest = Principal + Amount}$

Used for getting the compound Interest, Amount and Principal

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