Question:
Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7560
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 = $7560 – $4200 = $3360
Thus, Simple Interest = $3360
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 × 3360/4200 × 8
= 336000/33600
= 10 years (using formula)
Thus, Time (T) = 10 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) = 8% per annum
Simple Interest = $3360 (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 = 8% of Principal
= 8% of $4200
= 8/100 × 4200
= 8 × 4200/100
= 33600/100 = 336
Thus, simple Interest for 1 year = $336
Now,
∵ If the simple Interest is $336, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/336 years
∴ If the simple Interest is $3360, then the time = 1/336 × 3360 years
= 1 × 3360/336 years
= 3360/336 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(3) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?
(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(8) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(10) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.