Question:
Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9184
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 = $9184 – $5600 = $3584
Thus, Simple Interest = $3584
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 × 3584/5600 × 8
= 358400/44800
= 8 years (using formula)
Thus, Time (T) = 8 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) = $5600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3584 (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 $5600
= 8/100 × 5600
= 8 × 5600/100
= 44800/100 = 448
Thus, simple Interest for 1 year = $448
Now,
∵ If the simple Interest is $448, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/448 years
∴ If the simple Interest is $3584, then the time = 1/448 × 3584 years
= 1 × 3584/448 years
= 3584/448 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.
(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(3) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(5) 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.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?
(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?