Question:
What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?
Correct Answer
$5041
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 6
= $3550 ×7/100 × 6
= 3550 × 7 × 6/100
= 24850 × 6/100
= 149100/100
= $1491
Thus, Simple Interest = $1491
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 + $1491
= $5041
Thus, Amount to be paid = $5041 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3550 + ($3550 × 7% × 6)
= $3550 + ($3550 ×7/100 × 6)
= $3550 + (3550 × 7 × 6/100)
= $3550 + (24850 × 6/100)
= $3550 + (149100/100)
= $3550 + $1491 = $5041
Thus, Amount (A) to be paid = $5041 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3550, the simple interest in 1 year
= 7/100 × 3550
= 7 × 3550/100
= 24850/100 = $248.5
Thus, simple interest for 1 year = $248.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $248.5 × 6 = $1491
Thus, Simple Interest (SI) = $1491
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $1491
= $5041
Thus, Amount to be paid = $5041 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(2) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(10) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.