Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
Correct Answer
$7085
Solution And Explanation
Solution
Given,
Principal (P) = $5450
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) = $5450 × 3% × 10
= $5450 ×3/100 × 10
= 5450 × 3 × 10/100
= 16350 × 10/100
= 163500/100
= $1635
Thus, Simple Interest = $1635
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 = $5450 + $1635
= $7085
Thus, Amount to be paid = $7085 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 = $5450
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 3% × 10)
= $5450 + ($5450 ×3/100 × 10)
= $5450 + (5450 × 3 × 10/100)
= $5450 + (16350 × 10/100)
= $5450 + (163500/100)
= $5450 + $1635 = $7085
Thus, Amount (A) to be paid = $7085 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 $5450, the simple interest in 1 year
= 3/100 × 5450
= 3 × 5450/100
= 16350/100 = $163.5
Thus, simple interest for 1 year = $163.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $163.5 × 10 = $1635
Thus, Simple Interest (SI) = $1635
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1635
= $7085
Thus, Amount to be paid = $7085 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(4) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(7) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(8) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.