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) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(10) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?