Question:
Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9350
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 = $9350 – $5500 = $3850
Thus, Simple Interest = $3850
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 × 3850/5500 × 7
= 385000/38500
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5500
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3850 (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 = 7% of Principal
= 7% of $5500
= 7/100 × 5500
= 7 × 5500/100
= 38500/100 = 385
Thus, simple Interest for 1 year = $385
Now,
∵ If the simple Interest is $385, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/385 years
∴ If the simple Interest is $3850, then the time = 1/385 × 3850 years
= 1 × 3850/385 years
= 3850/385 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(3) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(6) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(9) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?