Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
Correct Answer
$11700
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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) = $5850 × 10% × 10
= $5850 ×10/100 × 10
= 5850 × 10 × 10/100
= 58500 × 10/100
= 585000/100
= $5850
Thus, Simple Interest = $5850
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 = $5850 + $5850
= $11700
Thus, Amount to be paid = $11700 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 = $5850
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 10% × 10)
= $5850 + ($5850 ×10/100 × 10)
= $5850 + (5850 × 10 × 10/100)
= $5850 + (58500 × 10/100)
= $5850 + (585000/100)
= $5850 + $5850 = $11700
Thus, Amount (A) to be paid = $11700 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 $5850, the simple interest in 1 year
= 10/100 × 5850
= 10 × 5850/100
= 58500/100 = $585
Thus, simple interest for 1 year = $585
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $585 × 10 = $5850
Thus, Simple Interest (SI) = $5850
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $5850
= $11700
Thus, Amount to be paid = $11700 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(4) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(6) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.