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) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.
(6) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
(9) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.