Question:
Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 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) = 9% per annum
Amount (A) = $10450
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 = $10450 – $5500 = $4950
Thus, Simple Interest = $4950
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 × 4950/5500 × 9
= 495000/49500
= 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) = 9% per annum
Simple Interest = $4950 (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 $5500
= 9/100 × 5500
= 9 × 5500/100
= 49500/100 = 495
Thus, simple Interest for 1 year = $495
Now,
∵ If the simple Interest is $495, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/495 years
∴ If the simple Interest is $4950, then the time = 1/495 × 4950 years
= 1 × 4950/495 years
= 4950/495 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(3) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.
(4) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(7) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.