Question:
Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7990
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 = $7990 – $4700 = $3290
Thus, Simple Interest = $3290
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 × 3290/4700 × 10
= 329000/47000
= 7 years (using formula)
Thus, Time (T) = 7 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) = 10% per annum
Simple Interest = $3290 (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 $4700
= 10/100 × 4700
= 10 × 4700/100
= 47000/100 = 470
Thus, simple Interest for 1 year = $470
Now,
∵ If the simple Interest is $470, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/470 years
∴ If the simple Interest is $3290, then the time = 1/470 × 3290 years
= 1 × 3290/470 years
= 3290/470 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.