Question:
Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6390
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 = $6390 – $4500 = $1890
Thus, Simple Interest = $1890
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 × 1890/4500 × 6
= 189000/27000
= 7 years (using formula)
Thus, Time (T) = 7 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 = $1890 (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 $1890, then the time = 1/270 × 1890 years
= 1 × 1890/270 years
= 1890/270 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(9) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.