Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
Correct Answer
$5106
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 8%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 6
= $3450 ×8/100 × 6
= 3450 × 8 × 6/100
= 27600 × 6/100
= 165600/100
= $1656
Thus, Simple Interest = $1656
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 + $1656
= $5106
Thus, Amount to be paid = $5106 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) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 8% × 6)
= $3450 + ($3450 ×8/100 × 6)
= $3450 + (3450 × 8 × 6/100)
= $3450 + (27600 × 6/100)
= $3450 + (165600/100)
= $3450 + $1656 = $5106
Thus, Amount (A) to be paid = $5106 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3450, the simple interest in 1 year
= 8/100 × 3450
= 8 × 3450/100
= 27600/100 = $276
Thus, simple interest for 1 year = $276
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $276 × 6 = $1656
Thus, Simple Interest (SI) = $1656
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1656
= $5106
Thus, Amount to be paid = $5106 Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(2) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(6) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(8) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.
(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?