Question:
Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 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) = 8% per annum
Amount (A) = $9176
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 = $9176 – $6200 = $2976
Thus, Simple Interest = $2976
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 × 2976/6200 × 8
= 297600/49600
= 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) = 8% per annum
Simple Interest = $2976 (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 $6200
= 8/100 × 6200
= 8 × 6200/100
= 49600/100 = 496
Thus, simple Interest for 1 year = $496
Now,
∵ If the simple Interest is $496, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/496 years
∴ If the simple Interest is $2976, then the time = 1/496 × 2976 years
= 1 × 2976/496 years
= 2976/496 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(5) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?
(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.