Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
Correct Answer
$7345
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 3%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 10
= $5650 ×3/100 × 10
= 5650 × 3 × 10/100
= 16950 × 10/100
= 169500/100
= $1695
Thus, Simple Interest = $1695
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 + $1695
= $7345
Thus, Amount to be paid = $7345 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) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 3% × 10)
= $5650 + ($5650 ×3/100 × 10)
= $5650 + (5650 × 3 × 10/100)
= $5650 + (16950 × 10/100)
= $5650 + (169500/100)
= $5650 + $1695 = $7345
Thus, Amount (A) to be paid = $7345 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5650, the simple interest in 1 year
= 3/100 × 5650
= 3 × 5650/100
= 16950/100 = $169.5
Thus, simple interest for 1 year = $169.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $169.5 × 10 = $1695
Thus, Simple Interest (SI) = $1695
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1695
= $7345
Thus, Amount to be paid = $7345 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(3) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(7) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.
(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(10) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.