Question:
Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8280
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 = $8280 – $4600 = $3680
Thus, Simple Interest = $3680
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 × 3680/4600 × 8
= 368000/36800
= 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) = $4600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3680 (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 = 8% of Principal
= 8% of $4600
= 8/100 × 4600
= 8 × 4600/100
= 36800/100 = 368
Thus, simple Interest for 1 year = $368
Now,
∵ If the simple Interest is $368, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/368 years
∴ If the simple Interest is $3680, then the time = 1/368 × 3680 years
= 1 × 3680/368 years
= 3680/368 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.