Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
Correct Answer
$4508.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 9%
Time (t) = 3 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) = $3550 × 9% × 3
= $3550 ×9/100 × 3
= 3550 × 9 × 3/100
= 31950 × 3/100
= 95850/100
= $958.5
Thus, Simple Interest = $958.5
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 = $3550 + $958.5
= $4508.5
Thus, Amount to be paid = $4508.5 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 = $3550
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 9% × 3)
= $3550 + ($3550 ×9/100 × 3)
= $3550 + (3550 × 9 × 3/100)
= $3550 + (31950 × 3/100)
= $3550 + (95850/100)
= $3550 + $958.5 = $4508.5
Thus, Amount (A) to be paid = $4508.5 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 $3550, the simple interest in 1 year
= 9/100 × 3550
= 9 × 3550/100
= 31950/100 = $319.5
Thus, simple interest for 1 year = $319.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $319.5 × 3 = $958.5
Thus, Simple Interest (SI) = $958.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $958.5
= $4508.5
Thus, Amount to be paid = $4508.5 Answer
Similar Questions
(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(4) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(6) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(9) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?