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) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(4) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(6) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.