Question:
Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7980
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 = $7980 – $4200 = $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 × 3780/4200 × 10
= 378000/42000
= 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) = $4200
Rate of Simple Interest (R) = 10% 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 = 10% of Principal
= 10% of $4200
= 10/100 × 4200
= 10 × 4200/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $3780, then the time = 1/420 × 3780 years
= 1 × 3780/420 years
= 3780/420 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(2) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(5) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(8) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.