Question:
Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10540
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 = $10540 – $6200 = $4340
Thus, Simple Interest = $4340
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 × 4340/6200 × 7
= 434000/43400
= 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) = $6200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4340 (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 = 7% of Principal
= 7% of $6200
= 7/100 × 6200
= 7 × 6200/100
= 43400/100 = 434
Thus, simple Interest for 1 year = $434
Now,
∵ If the simple Interest is $434, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/434 years
∴ If the simple Interest is $4340, then the time = 1/434 × 4340 years
= 1 × 4340/434 years
= 4340/434 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(7) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.