Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
Correct Answer
$5520
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $3450 × 10% × 6
= $3450 ×10/100 × 6
= 3450 × 10 × 6/100
= 34500 × 6/100
= 207000/100
= $2070
Thus, Simple Interest = $2070
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 = $3450 + $2070
= $5520
Thus, Amount to be paid = $5520 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 = $3450
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 10% × 6)
= $3450 + ($3450 ×10/100 × 6)
= $3450 + (3450 × 10 × 6/100)
= $3450 + (34500 × 6/100)
= $3450 + (207000/100)
= $3450 + $2070 = $5520
Thus, Amount (A) to be paid = $5520 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3450, the simple interest in 1 year
= 10/100 × 3450
= 10 × 3450/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $345 × 6 = $2070
Thus, Simple Interest (SI) = $2070
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $2070
= $5520
Thus, Amount to be paid = $5520 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(4) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(8) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.