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) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.