Question:
Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7520
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 = $7520 – $4700 = $2820
Thus, Simple Interest = $2820
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 × 2820/4700 × 10
= 282000/47000
= 6 years (using formula)
Thus, Time (T) = 6 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) = 10% per annum
Simple Interest = $2820 (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 = 10% of Principal
= 10% of $4700
= 10/100 × 4700
= 10 × 4700/100
= 47000/100 = 470
Thus, simple Interest for 1 year = $470
Now,
∵ If the simple Interest is $470, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/470 years
∴ If the simple Interest is $2820, then the time = 1/470 × 2820 years
= 1 × 2820/470 years
= 2820/470 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(8) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.