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) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.