Question:
Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9360
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 = $9360 – $5200 = $4160
Thus, Simple Interest = $4160
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 × 4160/5200 × 10
= 416000/52000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $5200
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4160 (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 $5200
= 10/100 × 5200
= 10 × 5200/100
= 52000/100 = 520
Thus, simple Interest for 1 year = $520
Now,
∵ If the simple Interest is $520, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/520 years
∴ If the simple Interest is $4160, then the time = 1/520 × 4160 years
= 1 × 4160/520 years
= 4160/520 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(4) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(6) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.