Question:
Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $11180
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 = $11180 – $6500 = $4680
Thus, Simple Interest = $4680
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 × 4680/6500 × 8
= 468000/52000
= 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) = $6500
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4680 (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 $6500
= 8/100 × 6500
= 8 × 6500/100
= 52000/100 = 520
Thus, simple Interest for 1 year = $520
Now,
∵ If the simple Interest is $520, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/520 years
∴ If the simple Interest is $4680, then the time = 1/520 × 4680 years
= 1 × 4680/520 years
= 4680/520 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(7) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(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 Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.