Question:
Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7790
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 = $7790 – $4100 = $3690
Thus, Simple Interest = $3690
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 × 3690/4100 × 10
= 369000/41000
= 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) = $4100
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3690 (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 $4100
= 10/100 × 4100
= 10 × 4100/100
= 41000/100 = 410
Thus, simple Interest for 1 year = $410
Now,
∵ If the simple Interest is $410, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/410 years
∴ If the simple Interest is $3690, then the time = 1/410 × 3690 years
= 1 × 3690/410 years
= 3690/410 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?