Question:
( 1 of 10 ) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
9
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7696
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 = $7696 – $5200 = $2496
Thus, Simple Interest = $2496
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 × 2496/5200 × 8
= 249600/41600
= 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) = $5200
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2496 (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 $5200
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = 416
Thus, simple Interest for 1 year = $416
Now,
∵ If the simple Interest is $416, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/416 years
∴ If the simple Interest is $2496, then the time = 1/416 × 2496 years
= 1 × 2496/416 years
= 2496/416 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(3) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(4) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(7) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 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 3% simple interest for 8 years.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.
(10) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?