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) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(5) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.