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) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(7) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?