Question:
Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7912
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 = $7912 – $4600 = $3312
Thus, Simple Interest = $3312
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 × 3312/4600 × 8
= 331200/36800
= 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) = $4600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3312 (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 = 8% of Principal
= 8% of $4600
= 8/100 × 4600
= 8 × 4600/100
= 36800/100 = 368
Thus, simple Interest for 1 year = $368
Now,
∵ If the simple Interest is $368, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/368 years
∴ If the simple Interest is $3312, then the time = 1/368 × 3312 years
= 1 × 3312/368 years
= 3312/368 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(3) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(8) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.