Question:
Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8507
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 = $8507 – $4700 = $3807
Thus, Simple Interest = $3807
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 × 3807/4700 × 9
= 380700/42300
= 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) = $4700
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3807 (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 $4700
= 9/100 × 4700
= 9 × 4700/100
= 42300/100 = 423
Thus, simple Interest for 1 year = $423
Now,
∵ If the simple Interest is $423, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/423 years
∴ If the simple Interest is $3807, then the time = 1/423 × 3807 years
= 1 × 3807/423 years
= 3807/423 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(3) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(4) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(8) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?