Question:
Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $13110
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 = $13110 – $6900 = $6210
Thus, Simple Interest = $6210
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 × 6210/6900 × 10
= 621000/69000
= 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) = $6900
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6210 (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 = 10% of Principal
= 10% of $6900
= 10/100 × 6900
= 10 × 6900/100
= 69000/100 = 690
Thus, simple Interest for 1 year = $690
Now,
∵ If the simple Interest is $690, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/690 years
∴ If the simple Interest is $6210, then the time = 1/690 × 6210 years
= 1 × 6210/690 years
= 6210/690 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(3) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(8) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.