Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
Correct Answer
$9128
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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) = $5600 × 7% × 9
= $5600 ×7/100 × 9
= 5600 × 7 × 9/100
= 39200 × 9/100
= 352800/100
= $3528
Thus, Simple Interest = $3528
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 = $5600 + $3528
= $9128
Thus, Amount to be paid = $9128 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 = $5600
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 7% × 9)
= $5600 + ($5600 ×7/100 × 9)
= $5600 + (5600 × 7 × 9/100)
= $5600 + (39200 × 9/100)
= $5600 + (352800/100)
= $5600 + $3528 = $9128
Thus, Amount (A) to be paid = $9128 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 $5600, the simple interest in 1 year
= 7/100 × 5600
= 7 × 5600/100
= 39200/100 = $392
Thus, simple interest for 1 year = $392
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $392 × 9 = $3528
Thus, Simple Interest (SI) = $3528
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $3528
= $9128
Thus, Amount to be paid = $9128 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(3) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(7) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(10) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?