Question:
John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $6776
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 = $6776 – $4400 = $2376
Thus, Simple Interest = $2376
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 × 2376/4400 × 9
= 237600/39600
= 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) = $4400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2376 (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 = 9% of Principal
= 9% of $4400
= 9/100 × 4400
= 9 × 4400/100
= 39600/100 = 396
Thus, simple Interest for 1 year = $396
Now,
∵ If the simple Interest is $396, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/396 years
∴ If the simple Interest is $2376, then the time = 1/396 × 2376 years
= 1 × 2376/396 years
= 2376/396 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(3) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(6) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?
(7) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?