Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
Correct Answer
$7458
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5650 × 4% × 8
= $5650 ×4/100 × 8
= 5650 × 4 × 8/100
= 22600 × 8/100
= 180800/100
= $1808
Thus, Simple Interest = $1808
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 = $5650 + $1808
= $7458
Thus, Amount to be paid = $7458 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 = $5650
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 4% × 8)
= $5650 + ($5650 ×4/100 × 8)
= $5650 + (5650 × 4 × 8/100)
= $5650 + (22600 × 8/100)
= $5650 + (180800/100)
= $5650 + $1808 = $7458
Thus, Amount (A) to be paid = $7458 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5650, the simple interest in 1 year
= 4/100 × 5650
= 4 × 5650/100
= 22600/100 = $226
Thus, simple interest for 1 year = $226
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $226 × 8 = $1808
Thus, Simple Interest (SI) = $1808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1808
= $7458
Thus, Amount to be paid = $7458 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(2) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(5) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(8) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?
(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.