In what time will a sum of money lent at 8 1/3 simple interest becomes 4 times of itself

Q: What sum of money lent out at 5% for 3 years will produce the same interest as Rupees 900 lent out at 4% for 5 years?

∴ S I = P R T 100 = 900 × 4 × 5 100 = 180 R s . ∴SI=frac{PRT}{100}=frac{900times4times5}{100}=180Rs. ∴SI=100PRT=100900×4×5=180Rs.

A sum of money, lent out at simple interest, doubles itself in 8 years. Find :
(i) the rate of interest
(ii) in how many years will the sum become triple (three times) of itself at the same rate percent?

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Let the rate of interest is r and sum of money be x it becomes 4x3 in 6 yrsSo, SI in 6 yrs =4x3−x=x3As we know that SI =ptr100, where p=x, t=6. or x3=x×6×r100 or r=509 ∴r=5.56% (approx)So, rate of interest 5.56%
In what time will a sum of money lent at 8 1 3 simple interest becomes 4 times of itself?
What sum of money lent out at 5% for 3 years will produce the same interest as Rupees 900 lent out at 4% for 5 years?
What sum of money lent for 3 year at 4% a year will to Rupee 392?
What should be the interest rate for an amount to become 4 times of itself at simple interest in 60 years?

Solution

Let P = Rs.100, A = Rs.200

I = Rs.200 − Rs.100 = Rs.100, T = 8 years

R =`(100xx"I")/("P"xx"T")=(100xx100)/(100xx8)`

`=100/8=25/2%`

Now again P = Rs.100

A = Rs.300

I = Rs.300 − Rs.100 = Rs.200

R = `25/2%`

T =`(100xx"I")/("P"xx"R")=(100xx200)/(100xx25/2)=(100xx200xx2)/(100xx25)`

= 16 Years

So the given sum of money will become triple in 16 years.

Concept: Concept of Principal, Interest, Amount, and Simple Interest

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A sum of money becomes 4 / 3 of itself in 6 years at a certain rate of simple interest find the rate of interest.

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Solution

Let the rate of interest is r and sum of money be x it becomes 4x3 in 6 yrsSo, SI in 6 yrs =4x3−x=x3As we know that SI =ptr100, where p=x, t=6. or x3=x×6×r100 or r=509 ∴r=5.56% (approx)So, rate of interest 5.56%

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