Question:
Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9231
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 = $9231 – $5100 = $4131
Thus, Simple Interest = $4131
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 × 4131/5100 × 9
= 413100/45900
= 9 years (using formula)
Thus, Time (T) = 9 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) = $5100
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4131 (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 $5100
= 9/100 × 5100
= 9 × 5100/100
= 45900/100 = 459
Thus, simple Interest for 1 year = $459
Now,
∵ If the simple Interest is $459, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/459 years
∴ If the simple Interest is $4131, then the time = 1/459 × 4131 years
= 1 × 4131/459 years
= 4131/459 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(4) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(6) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?