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) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?
(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(10) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?