Question:
Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $11340
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 = $11340 – $6300 = $5040
Thus, Simple Interest = $5040
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 × 5040/6300 × 8
= 504000/50400
= 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) = $6300
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $5040 (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 $6300
= 8/100 × 6300
= 8 × 6300/100
= 50400/100 = 504
Thus, simple Interest for 1 year = $504
Now,
∵ If the simple Interest is $504, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/504 years
∴ If the simple Interest is $5040, then the time = 1/504 × 5040 years
= 1 × 5040/504 years
= 5040/504 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(4) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.
(5) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(7) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
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