Question:
( 1 of 10 ) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
10.5
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7384
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 = $7384 – $5200 = $2184
Thus, Simple Interest = $2184
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 × 2184/5200 × 6
= 218400/31200
= 7 years (using formula)
Thus, Time (T) = 7 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) = 6% per annum
Simple Interest = $2184 (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 = 6% of Principal
= 6% of $5200
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = 312
Thus, simple Interest for 1 year = $312
Now,
∵ If the simple Interest is $312, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/312 years
∴ If the simple Interest is $2184, then the time = 1/312 × 2184 years
= 1 × 2184/312 years
= 2184/312 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 4% simple interest?
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(4) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(6) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(9) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?