Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
Correct Answer
$11210
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5900 ×10/100 × 9
= 5900 × 10 × 9/100
= 59000 × 9/100
= 531000/100
= $5310
Thus, Simple Interest = $5310
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 + $5310
= $11210
Thus, Amount to be paid = $11210 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) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 10% × 9)
= $5900 + ($5900 ×10/100 × 9)
= $5900 + (5900 × 10 × 9/100)
= $5900 + (59000 × 9/100)
= $5900 + (531000/100)
= $5900 + $5310 = $11210
Thus, Amount (A) to be paid = $11210 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 9 years
= Simple interest for 1 year × 9
= $590 × 9 = $5310
Thus, Simple Interest (SI) = $5310
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $5310
= $11210
Thus, Amount to be paid = $11210 Answer
Similar Questions
(1) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(6) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.