Question:
( 1 of 10 ) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
10.5
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6958
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 = $6958 – $4900 = $2058
Thus, Simple Interest = $2058
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 × 2058/4900 × 6
= 205800/29400
= 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) = 6% per annum
Simple Interest = $2058 (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 = 6% of Principal
= 6% of $4900
= 6/100 × 4900
= 6 × 4900/100
= 29400/100 = 294
Thus, simple Interest for 1 year = $294
Now,
∵ If the simple Interest is $294, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/294 years
∴ If the simple Interest is $2058, then the time = 1/294 × 2058 years
= 1 × 2058/294 years
= 2058/294 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
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(2) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(8) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
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