Question:
Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7380
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 = $7380 – $4100 = $3280
Thus, Simple Interest = $3280
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 × 3280/4100 × 8
= 328000/32800
= 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) = $4100
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3280 (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 $4100
= 8/100 × 4100
= 8 × 4100/100
= 32800/100 = 328
Thus, simple Interest for 1 year = $328
Now,
∵ If the simple Interest is $328, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/328 years
∴ If the simple Interest is $3280, then the time = 1/328 × 3280 years
= 1 × 3280/328 years
= 3280/328 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(7) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.