Question:
( 1 of 10 ) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 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) = $6600
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10560
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 = $10560 – $6600 = $3960
Thus, Simple Interest = $3960
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 × 3960/6600 × 10
= 396000/66000
= 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) = $6600
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3960 (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 = 10% of Principal
= 10% of $6600
= 10/100 × 6600
= 10 × 6600/100
= 66000/100 = 660
Thus, simple Interest for 1 year = $660
Now,
∵ If the simple Interest is $660, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/660 years
∴ If the simple Interest is $3960, then the time = 1/660 × 3960 years
= 1 × 3960/660 years
= 3960/660 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
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(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(3) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.