Question:
Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8432
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 = $8432 – $6200 = $2232
Thus, Simple Interest = $2232
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 × 2232/6200 × 6
= 223200/37200
= 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) = $6200
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2232 (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 = 6% of Principal
= 6% of $6200
= 6/100 × 6200
= 6 × 6200/100
= 37200/100 = 372
Thus, simple Interest for 1 year = $372
Now,
∵ If the simple Interest is $372, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/372 years
∴ If the simple Interest is $2232, then the time = 1/372 × 2232 years
= 1 × 2232/372 years
= 2232/372 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(4) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(9) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?