Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
Correct Answer
$9040
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 10
= $5650 ×6/100 × 10
= 5650 × 6 × 10/100
= 33900 × 10/100
= 339000/100
= $3390
Thus, Simple Interest = $3390
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 + $3390
= $9040
Thus, Amount to be paid = $9040 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 6% × 10)
= $5650 + ($5650 ×6/100 × 10)
= $5650 + (5650 × 6 × 10/100)
= $5650 + (33900 × 10/100)
= $5650 + (339000/100)
= $5650 + $3390 = $9040
Thus, Amount (A) to be paid = $9040 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5650, the simple interest in 1 year
= 6/100 × 5650
= 6 × 5650/100
= 33900/100 = $339
Thus, simple interest for 1 year = $339
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $339 × 10 = $3390
Thus, Simple Interest (SI) = $3390
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3390
= $9040
Thus, Amount to be paid = $9040 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(2) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
(6) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.