Question:
( 1 of 10 ) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
15
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12600
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 = $12600 – $6300 = $6300
Thus, Simple Interest = $6300
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 × 6300/6300 × 10
= 630000/63000
= 10 years (using formula)
Thus, Time (T) = 10 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) = $6300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6300 (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 $6300
= 10/100 × 6300
= 10 × 6300/100
= 63000/100 = 630
Thus, simple Interest for 1 year = $630
Now,
∵ If the simple Interest is $630, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/630 years
∴ If the simple Interest is $6300, then the time = 1/630 × 6300 years
= 1 × 6300/630 years
= 6300/630 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
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