Question:
Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7546
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 = $7546 – $4900 = $2646
Thus, Simple Interest = $2646
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 × 2646/4900 × 6
= 264600/29400
= 9 years (using formula)
Thus, Time (T) = 9 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 = $2646 (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 $2646, then the time = 1/294 × 2646 years
= 1 × 2646/294 years
= 2646/294 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(2) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(4) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.
(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(10) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.