Question:
Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 7% 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 × 7
= 205800/34300
= 6 years (using formula)
Thus, Time (T) = 6 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 = $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 = 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 $2058, then the time = 1/343 × 2058 years
= 1 × 2058/343 years
= 2058/343 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(4) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(5) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(7) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?