Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
Correct Answer
$9440
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $5900 ×6/100 × 10
= 5900 × 6 × 10/100
= 35400 × 10/100
= 354000/100
= $3540
Thus, Simple Interest = $3540
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 + $3540
= $9440
Thus, Amount to be paid = $9440 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 6% × 10)
= $5900 + ($5900 ×6/100 × 10)
= $5900 + (5900 × 6 × 10/100)
= $5900 + (35400 × 10/100)
= $5900 + (354000/100)
= $5900 + $3540 = $9440
Thus, Amount (A) to be paid = $9440 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5900, the simple interest in 1 year
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = $354
Thus, simple interest for 1 year = $354
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $354 × 10 = $3540
Thus, Simple Interest (SI) = $3540
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3540
= $9440
Thus, Amount to be paid = $9440 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.
(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(6) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(7) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(9) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?