Question:
Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8330
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 = $8330 – $4900 = $3430
Thus, Simple Interest = $3430
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 × 3430/4900 × 7
= 343000/34300
= 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) = $4900
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3430 (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 = 7% of Principal
= 7% of $4900
= 7/100 × 4900
= 7 × 4900/100
= 34300/100 = 343
Thus, simple Interest for 1 year = $343
Now,
∵ If the simple Interest is $343, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/343 years
∴ If the simple Interest is $3430, then the time = 1/343 × 3430 years
= 1 × 3430/343 years
= 3430/343 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(5) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(8) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.