Question:
David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8160
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 = $8160 – $4800 = $3360
Thus, Simple Interest = $3360
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 × 3360/4800 × 10
= 336000/48000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4800
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3360 (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 = 10% of Principal
= 10% of $4800
= 10/100 × 4800
= 10 × 4800/100
= 48000/100 = 480
Thus, simple Interest for 1 year = $480
Now,
∵ If the simple Interest is $480, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/480 years
∴ If the simple Interest is $3360, then the time = 1/480 × 3360 years
= 1 × 3360/480 years
= 3360/480 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(4) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.
(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(8) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?