Question:
If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$4160
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 2%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $4000 × 2% × 2
= $4000 ×2/100 × 2
= 4000 × 2 × 2/100
= 8000 × 2/100
= 16000/100
= $160
Thus, Simple Interest = $160
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $160
= $4160
Thus, Amount to be paid = $4160 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $4000
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 2 years
Thus, Amount (A)
= $4000 + ($4000 × 2% × 2)
= $4000 + ($4000 ×2/100 × 2)
= $4000 + (4000 × 2 × 2/100)
= $4000 + (8000 × 2/100)
= $4000 + (16000/100)
= $4000 + $160 = $4160
Thus, Amount (A) to be paid = $4160 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest in 1 year = $2
∴ For $1, the simple interest in 1 year = 2/100
∴ For $4000, the simple interest in 1 year
= 2/100 × 4000
= 2 × 4000/100
= 8000/100 = $80
Thus, simple interest in 1 year = $80
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $80 × 2 = $160
Thus, Simple Interest (SI) = $160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $160
= $4160
Thus, Amount to be paid = $4160 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 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 3% simple interest for 8 years.
(4) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(9) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.