Question:
Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6068
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 = $6068 – $4100 = $1968
Thus, Simple Interest = $1968
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 × 1968/4100 × 8
= 196800/32800
= 6 years (using formula)
Thus, Time (T) = 6 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 = $1968 (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 $1968, then the time = 1/328 × 1968 years
= 1 × 1968/328 years
= 1968/328 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(2) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(4) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.