Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
Correct Answer
$10735
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5650 ×9/100 × 10
= 5650 × 9 × 10/100
= 50850 × 10/100
= 508500/100
= $5085
Thus, Simple Interest = $5085
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 + $5085
= $10735
Thus, Amount to be paid = $10735 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 9% × 10)
= $5650 + ($5650 ×9/100 × 10)
= $5650 + (5650 × 9 × 10/100)
= $5650 + (50850 × 10/100)
= $5650 + (508500/100)
= $5650 + $5085 = $10735
Thus, Amount (A) to be paid = $10735 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5650, the simple interest in 1 year
= 9/100 × 5650
= 9 × 5650/100
= 50850/100 = $508.5
Thus, simple interest for 1 year = $508.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $508.5 × 10 = $5085
Thus, Simple Interest (SI) = $5085
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $5085
= $10735
Thus, Amount to be paid = $10735 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.