Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
Correct Answer
$9605
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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) = $5650 × 10% × 7
= $5650 ×10/100 × 7
= 5650 × 10 × 7/100
= 56500 × 7/100
= 395500/100
= $3955
Thus, Simple Interest = $3955
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 + $3955
= $9605
Thus, Amount to be paid = $9605 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5650 + ($5650 × 10% × 7)
= $5650 + ($5650 ×10/100 × 7)
= $5650 + (5650 × 10 × 7/100)
= $5650 + (56500 × 7/100)
= $5650 + (395500/100)
= $5650 + $3955 = $9605
Thus, Amount (A) to be paid = $9605 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 $5650, the simple interest in 1 year
= 10/100 × 5650
= 10 × 5650/100
= 56500/100 = $565
Thus, simple interest for 1 year = $565
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $565 × 7 = $3955
Thus, Simple Interest (SI) = $3955
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3955
= $9605
Thus, Amount to be paid = $9605 Answer
Similar Questions
(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(5) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(9) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.