Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
Correct Answer
$3869.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 3%
Time (t) = 3 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) = $3550 × 3% × 3
= $3550 ×3/100 × 3
= 3550 × 3 × 3/100
= 10650 × 3/100
= 31950/100
= $319.5
Thus, Simple Interest = $319.5
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 + $319.5
= $3869.5
Thus, Amount to be paid = $3869.5 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 3% × 3)
= $3550 + ($3550 ×3/100 × 3)
= $3550 + (3550 × 3 × 3/100)
= $3550 + (10650 × 3/100)
= $3550 + (31950/100)
= $3550 + $319.5 = $3869.5
Thus, Amount (A) to be paid = $3869.5 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 $3550, the simple interest in 1 year
= 3/100 × 3550
= 3 × 3550/100
= 10650/100 = $106.5
Thus, simple interest for 1 year = $106.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $106.5 × 3 = $319.5
Thus, Simple Interest (SI) = $319.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $319.5
= $3869.5
Thus, Amount to be paid = $3869.5 Answer
Similar Questions
(1) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(8) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?
(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.