Question:
Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8313
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 = $8313 – $5100 = $3213
Thus, Simple Interest = $3213
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 × 3213/5100 × 9
= 321300/45900
= 7 years (using formula)
Thus, Time (T) = 7 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 = $3213 (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 $3213, then the time = 1/459 × 3213 years
= 1 × 3213/459 years
= 3213/459 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(3) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?
(5) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(9) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.