Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
Correct Answer
$8475
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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% × 10
= $5650 ×5/100 × 10
= 5650 × 5 × 10/100
= 28250 × 10/100
= 282500/100
= $2825
Thus, Simple Interest = $2825
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 + $2825
= $8475
Thus, Amount to be paid = $8475 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) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 5% × 10)
= $5650 + ($5650 ×5/100 × 10)
= $5650 + (5650 × 5 × 10/100)
= $5650 + (28250 × 10/100)
= $5650 + (282500/100)
= $5650 + $2825 = $8475
Thus, Amount (A) to be paid = $8475 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 10 years
= Simple interest for 1 year × 10
= $282.5 × 10 = $2825
Thus, Simple Interest (SI) = $2825
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2825
= $8475
Thus, Amount to be paid = $8475 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.
(2) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?
(4) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(5) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?
(6) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(7) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(8) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.