Question:
Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7332
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 = $7332 – $4700 = $2632
Thus, Simple Interest = $2632
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 × 2632/4700 × 7
= 263200/32900
= 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) = $4700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2632 (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 $4700
= 7/100 × 4700
= 7 × 4700/100
= 32900/100 = 329
Thus, simple Interest for 1 year = $329
Now,
∵ If the simple Interest is $329, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/329 years
∴ If the simple Interest is $2632, then the time = 1/329 × 2632 years
= 1 × 2632/329 years
= 2632/329 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?
(6) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.