Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
Correct Answer
$6554
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5650 × 2% × 8
= $5650 ×2/100 × 8
= 5650 × 2 × 8/100
= 11300 × 8/100
= 90400/100
= $904
Thus, Simple Interest = $904
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 = $5650 + $904
= $6554
Thus, Amount to be paid = $6554 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 = $5650
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 2% × 8)
= $5650 + ($5650 ×2/100 × 8)
= $5650 + (5650 × 2 × 8/100)
= $5650 + (11300 × 8/100)
= $5650 + (90400/100)
= $5650 + $904 = $6554
Thus, Amount (A) to be paid = $6554 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5650, the simple interest in 1 year
= 2/100 × 5650
= 2 × 5650/100
= 11300/100 = $113
Thus, simple interest for 1 year = $113
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $113 × 8 = $904
Thus, Simple Interest (SI) = $904
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $904
= $6554
Thus, Amount to be paid = $6554 Answer
Similar Questions
(1) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(9) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?