Question:
Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7644
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 = $7644 – $4900 = $2744
Thus, Simple Interest = $2744
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 × 2744/4900 × 7
= 274400/34300
= 8 years (using formula)
Thus, Time (T) = 8 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 = $2744 (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 $2744, then the time = 1/343 × 2744 years
= 1 × 2744/343 years
= 2744/343 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
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(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.