Question:
Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10836
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 = $10836 – $6300 = $4536
Thus, Simple Interest = $4536
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 × 4536/6300 × 9
= 453600/56700
= 8 years (using formula)
Thus, Time (T) = 8 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) = 9% per annum
Simple Interest = $4536 (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 = 9% of Principal
= 9% of $6300
= 9/100 × 6300
= 9 × 6300/100
= 56700/100 = 567
Thus, simple Interest for 1 year = $567
Now,
∵ If the simple Interest is $567, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/567 years
∴ If the simple Interest is $4536, then the time = 1/567 × 4536 years
= 1 × 4536/567 years
= 4536/567 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(6) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?