Question:
( 1 of 10 ) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
9
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10780
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 = $10780 – $7000 = $3780
Thus, Simple Interest = $3780
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 × 3780/7000 × 9
= 378000/63000
= 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) = $7000
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3780 (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 = 9% of Principal
= 9% of $7000
= 9/100 × 7000
= 9 × 7000/100
= 63000/100 = 630
Thus, simple Interest for 1 year = $630
Now,
∵ If the simple Interest is $630, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/630 years
∴ If the simple Interest is $3780, then the time = 1/630 × 3780 years
= 1 × 3780/630 years
= 3780/630 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(4) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.
(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
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(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.