Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
Correct Answer
$10030
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5900 ×7/100 × 10
= 5900 × 7 × 10/100
= 41300 × 10/100
= 413000/100
= $4130
Thus, Simple Interest = $4130
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 + $4130
= $10030
Thus, Amount to be paid = $10030 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 7% × 10)
= $5900 + ($5900 ×7/100 × 10)
= $5900 + (5900 × 7 × 10/100)
= $5900 + (41300 × 10/100)
= $5900 + (413000/100)
= $5900 + $4130 = $10030
Thus, Amount (A) to be paid = $10030 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5900, the simple interest in 1 year
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = $413
Thus, simple interest for 1 year = $413
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $413 × 10 = $4130
Thus, Simple Interest (SI) = $4130
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4130
= $10030
Thus, Amount to be paid = $10030 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(3) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(6) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?
(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?