Question:
Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10492
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 = $10492 – $6100 = $4392
Thus, Simple Interest = $4392
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 × 4392/6100 × 8
= 439200/48800
= 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) = $6100
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4392 (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 $6100
= 8/100 × 6100
= 8 × 6100/100
= 48800/100 = 488
Thus, simple Interest for 1 year = $488
Now,
∵ If the simple Interest is $488, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/488 years
∴ If the simple Interest is $4392, then the time = 1/488 × 4392 years
= 1 × 4392/488 years
= 4392/488 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(2) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(8) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.