Question:
( 1 of 10 ) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(A) 30.75 days
(B) 26 1331/2509 days or 26.53 days
(C) 13 1331/2509 days or 13.53 days
(D) 41 days
You selected
12
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7708
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 = $7708 – $4700 = $3008
Thus, Simple Interest = $3008
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 × 3008/4700 × 8
= 300800/37600
= 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) = 8% per annum
Simple Interest = $3008 (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 $3008, then the time = 1/376 × 3008 years
= 1 × 3008/376 years
= 3008/376 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(5) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?