Question:
Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $12060
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $12060 – $6700 = $5360
Thus, Simple Interest = $5360
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 5360/6700 × 8
= 536000/53600
= 10 years (using formula)
Thus, Time (T) = 10 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $6700
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $5360 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 8% of Principal
= 8% of $6700
= 8/100 × 6700
= 8 × 6700/100
= 53600/100 = 536
Thus, simple Interest for 1 year = $536
Now,
∵ If the simple Interest is $536, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/536 years
∴ If the simple Interest is $5360, then the time = 1/536 × 5360 years
= 1 × 5360/536 years
= 5360/536 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(6) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?
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