Question

At what rate per cent compound interest will the
sum of 3200 amount to 5529.60 in three years?​

Answer 1

Given:

Rs. 3200 amounts to Rs. 5529.50 in 3 years at compound interest.

To find:

The rate of compound interest.

Step-by-step explanation:

Let the rate of compound interest is r% per annum.

Then 3200 * (1 + r/100)^3 = 5529.60

or, (1 + r/100)^3 = 5529.60/3200

or, 1 + r/100 = 1.2

or, r/100 = 0.2

or, r = 20

Answer:

Rate of compound interest per year is 20%.

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Answer 2

To Find :- At what rate per cent compound interest will the

sum of 3200 amount to 5529.60 in three years ?

Solution :-

Let us assume that, rate of interest is R% per annum .

we know that, when rate is compounded annually, then,

• Amount = Principal * [ 1 + (rate/100) ]^(time) .

given,

• Principal = Rs.3200
• Amount = Rs.5529.60 .
• Rate = R % per annum.
• Time = 3 years.

So,

→ 5529.60 = 3200 * [ 1 + (R/100) ]³

→ (5529.6/3200) = [ 1 + (R/100) ]³

→ (55296/32000) = [ 1 + (R/100) ]³

→ (13824/8000) = [ 1 + (R/100) ]³

→ (24/20)³ = [ 1 + (R/100) ]³

→ [1 + (4/20)]³ = [ 1 + (R/100) ]³

→ [ 1 + (20/100) ]³ = [ 1 + (R/100) ]³

comparing we get,

→ R = 20 % .

Hence, Required rate of interest is 20% per annum.

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