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