Question:
Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.
Correct Answer
$6534
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 7 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% × 7
= $5400 ×3/100 × 7
= 5400 × 3 × 7/100
= 16200 × 7/100
= 113400/100
= $1134
Thus, Simple Interest = $1134
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 + $1134
= $6534
Thus, Amount to be paid = $6534 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) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 7)
= $5400 + ($5400 ×3/100 × 7)
= $5400 + (5400 × 3 × 7/100)
= $5400 + (16200 × 7/100)
= $5400 + (113400/100)
= $5400 + $1134 = $6534
Thus, Amount (A) to be paid = $6534 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 7 years
= Simple interest for 1 year × 7
= $162 × 7 = $1134
Thus, Simple Interest (SI) = $1134
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1134
= $6534
Thus, Amount to be paid = $6534 Answer
Similar Questions
(1) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(9) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.