Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
Correct Answer
$7552
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5900 × 4% × 7
= $5900 ×4/100 × 7
= 5900 × 4 × 7/100
= 23600 × 7/100
= 165200/100
= $1652
Thus, Simple Interest = $1652
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 = $5900 + $1652
= $7552
Thus, Amount to be paid = $7552 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 = $5900
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 4% × 7)
= $5900 + ($5900 ×4/100 × 7)
= $5900 + (5900 × 4 × 7/100)
= $5900 + (23600 × 7/100)
= $5900 + (165200/100)
= $5900 + $1652 = $7552
Thus, Amount (A) to be paid = $7552 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5900, the simple interest in 1 year
= 4/100 × 5900
= 4 × 5900/100
= 23600/100 = $236
Thus, simple interest for 1 year = $236
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $236 × 7 = $1652
Thus, Simple Interest (SI) = $1652
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1652
= $7552
Thus, Amount to be paid = $7552 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(3) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?