Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
Correct Answer
$11800
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 10%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 10
= $5900 ×10/100 × 10
= 5900 × 10 × 10/100
= 59000 × 10/100
= 590000/100
= $5900
Thus, Simple Interest = $5900
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 + $5900
= $11800
Thus, Amount to be paid = $11800 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) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 10% × 10)
= $5900 + ($5900 ×10/100 × 10)
= $5900 + (5900 × 10 × 10/100)
= $5900 + (59000 × 10/100)
= $5900 + (590000/100)
= $5900 + $5900 = $11800
Thus, Amount (A) to be paid = $11800 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5900, the simple interest in 1 year
= 10/100 × 5900
= 10 × 5900/100
= 59000/100 = $590
Thus, simple interest for 1 year = $590
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $590 × 10 = $5900
Thus, Simple Interest (SI) = $5900
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $5900
= $11800
Thus, Amount to be paid = $11800 Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(6) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(8) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(9) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?