Question:
Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6120
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 = $6120 – $4500 = $1620
Thus, Simple Interest = $1620
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 × 1620/4500 × 6
= 162000/27000
= 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) = $4500
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1620 (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 = 6% of Principal
= 6% of $4500
= 6/100 × 4500
= 6 × 4500/100
= 27000/100 = 270
Thus, simple Interest for 1 year = $270
Now,
∵ If the simple Interest is $270, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/270 years
∴ If the simple Interest is $1620, then the time = 1/270 × 1620 years
= 1 × 1620/270 years
= 1620/270 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(6) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(10) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.