Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.
Correct Answer
$7910
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5650 ×5/100 × 8
= 5650 × 5 × 8/100
= 28250 × 8/100
= 226000/100
= $2260
Thus, Simple Interest = $2260
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 + $2260
= $7910
Thus, Amount to be paid = $7910 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 5% × 8)
= $5650 + ($5650 ×5/100 × 8)
= $5650 + (5650 × 5 × 8/100)
= $5650 + (28250 × 8/100)
= $5650 + (226000/100)
= $5650 + $2260 = $7910
Thus, Amount (A) to be paid = $7910 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5650, the simple interest in 1 year
= 5/100 × 5650
= 5 × 5650/100
= 28250/100 = $282.5
Thus, simple interest for 1 year = $282.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $282.5 × 8 = $2260
Thus, Simple Interest (SI) = $2260
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2260
= $7910
Thus, Amount to be paid = $7910 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?
(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(4) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.