Question:
Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7020
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 = $7020 – $4500 = $2520
Thus, Simple Interest = $2520
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 × 2520/4500 × 7
= 252000/31500
= 8 years (using formula)
Thus, Time (T) = 8 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) = 7% per annum
Simple Interest = $2520 (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 = 7% of Principal
= 7% of $4500
= 7/100 × 4500
= 7 × 4500/100
= 31500/100 = 315
Thus, simple Interest for 1 year = $315
Now,
∵ If the simple Interest is $315, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/315 years
∴ If the simple Interest is $2520, then the time = 1/315 × 2520 years
= 1 × 2520/315 years
= 2520/315 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?
(3) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?
(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?