Question:
David took a loan of $4800 at the rate of 7% 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
10
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 7% 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 × 7
= 336000/33600
= 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) = $4800
Rate of Simple Interest (R) = 7% 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 = 7% of Principal
= 7% of $4800
= 7/100 × 4800
= 7 × 4800/100
= 33600/100 = 336
Thus, simple Interest for 1 year = $336
Now,
∵ If the simple Interest is $336, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/336 years
∴ If the simple Interest is $3360, then the time = 1/336 × 3360 years
= 1 × 3360/336 years
= 3360/336 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.
(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.