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) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(2) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(6) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(9) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.