Question:
Elizabeth took a loan of $4900 at the rate of 8% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 8% 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 × 8
= 274400/39200
= 7 years (using formula)
Thus, Time (T) = 7 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) = 8% 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 = 8% of Principal
= 8% of $4900
= 8/100 × 4900
= 8 × 4900/100
= 39200/100 = 392
Thus, simple Interest for 1 year = $392
Now,
∵ If the simple Interest is $392, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/392 years
∴ If the simple Interest is $2744, then the time = 1/392 × 2744 years
= 1 × 2744/392 years
= 2744/392 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(6) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.