Question:
What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
Correct Answer
$4828
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 6%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 6
= $3550 ×6/100 × 6
= 3550 × 6 × 6/100
= 21300 × 6/100
= 127800/100
= $1278
Thus, Simple Interest = $1278
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 + $1278
= $4828
Thus, Amount to be paid = $4828 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) = 6%
And, Time (t) = 6 years
Thus, Amount (A)
= $3550 + ($3550 × 6% × 6)
= $3550 + ($3550 ×6/100 × 6)
= $3550 + (3550 × 6 × 6/100)
= $3550 + (21300 × 6/100)
= $3550 + (127800/100)
= $3550 + $1278 = $4828
Thus, Amount (A) to be paid = $4828 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3550, the simple interest in 1 year
= 6/100 × 3550
= 6 × 3550/100
= 21300/100 = $213
Thus, simple interest for 1 year = $213
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $213 × 6 = $1278
Thus, Simple Interest (SI) = $1278
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $1278
= $4828
Thus, Amount to be paid = $4828 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(6) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(9) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(10) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.