Question:
Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7888
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 = $7888 – $5800 = $2088
Thus, Simple Interest = $2088
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 × 2088/5800 × 6
= 208800/34800
= 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) = $5800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2088 (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 $5800
= 6/100 × 5800
= 6 × 5800/100
= 34800/100 = 348
Thus, simple Interest for 1 year = $348
Now,
∵ If the simple Interest is $348, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/348 years
∴ If the simple Interest is $2088, then the time = 1/348 × 2088 years
= 1 × 2088/348 years
= 2088/348 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) David had to pay $3706 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 Michael borrowed a sum of $5300 at 3% simple interest for 8 years.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(4) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.
(9) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?