Question:
Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 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) = 8% per annum
Amount (A) = $6956
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 = $6956 – $4700 = $2256
Thus, Simple Interest = $2256
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 × 2256/4700 × 8
= 225600/37600
= 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) = 8% per annum
Simple Interest = $2256 (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 = 8% of Principal
= 8% of $4700
= 8/100 × 4700
= 8 × 4700/100
= 37600/100 = 376
Thus, simple Interest for 1 year = $376
Now,
∵ If the simple Interest is $376, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/376 years
∴ If the simple Interest is $2256, then the time = 1/376 × 2256 years
= 1 × 2256/376 years
= 2256/376 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(2) 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.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(5) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.