Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
Correct Answer
$8775
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5850 ×5/100 × 10
= 5850 × 5 × 10/100
= 29250 × 10/100
= 292500/100
= $2925
Thus, Simple Interest = $2925
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 + $2925
= $8775
Thus, Amount to be paid = $8775 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 5% × 10)
= $5850 + ($5850 ×5/100 × 10)
= $5850 + (5850 × 5 × 10/100)
= $5850 + (29250 × 10/100)
= $5850 + (292500/100)
= $5850 + $2925 = $8775
Thus, Amount (A) to be paid = $8775 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5850, the simple interest in 1 year
= 5/100 × 5850
= 5 × 5850/100
= 29250/100 = $292.5
Thus, simple interest for 1 year = $292.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $292.5 × 10 = $2925
Thus, Simple Interest (SI) = $2925
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2925
= $8775
Thus, Amount to be paid = $8775 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(10) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.