Question:
Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
Correct Answer
$6696
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5400 × 3% × 8
= $5400 ×3/100 × 8
= 5400 × 3 × 8/100
= 16200 × 8/100
= 129600/100
= $1296
Thus, Simple Interest = $1296
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 = $5400 + $1296
= $6696
Thus, Amount to be paid = $6696 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 = $5400
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 8)
= $5400 + ($5400 ×3/100 × 8)
= $5400 + (5400 × 3 × 8/100)
= $5400 + (16200 × 8/100)
= $5400 + (129600/100)
= $5400 + $1296 = $6696
Thus, Amount (A) to be paid = $6696 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $162 × 8 = $1296
Thus, Simple Interest (SI) = $1296
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1296
= $6696
Thus, Amount to be paid = $6696 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.
(2) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(8) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.