Question:
( 1 of 10 ) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
9
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7888
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 = $7888 – $5800 = $2088
Thus, Simple Interest = $2088
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 × 2088/5800 × 6
= 208800/34800
= 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) = $5800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2088 (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 $5800
= 6/100 × 5800
= 6 × 5800/100
= 34800/100 = 348
Thus, simple Interest for 1 year = $348
Now,
∵ If the simple Interest is $348, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/348 years
∴ If the simple Interest is $2088, then the time = 1/348 × 2088 years
= 1 × 2088/348 years
= 2088/348 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(4) James took a loan of $4000 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.
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(6) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(7) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.