Question:
Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4500
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8145
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 = $8145 – $4500 = $3645
Thus, Simple Interest = $3645
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 × 3645/4500 × 9
= 364500/40500
= 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) = $4500
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3645 (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 $4500
= 9/100 × 4500
= 9 × 4500/100
= 40500/100 = 405
Thus, simple Interest for 1 year = $405
Now,
∵ If the simple Interest is $405, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/405 years
∴ If the simple Interest is $3645, then the time = 1/405 × 3645 years
= 1 × 3645/405 years
= 3645/405 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(5) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?
(8) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(10) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.