Question:
Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
Correct Answer
$9975
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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) = $5250 × 10% × 9
= $5250 ×10/100 × 9
= 5250 × 10 × 9/100
= 52500 × 9/100
= 472500/100
= $4725
Thus, Simple Interest = $4725
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 = $5250 + $4725
= $9975
Thus, Amount to be paid = $9975 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 = $5250
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5250 + ($5250 × 10% × 9)
= $5250 + ($5250 ×10/100 × 9)
= $5250 + (5250 × 10 × 9/100)
= $5250 + (52500 × 9/100)
= $5250 + (472500/100)
= $5250 + $4725 = $9975
Thus, Amount (A) to be paid = $9975 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 $5250, the simple interest in 1 year
= 10/100 × 5250
= 10 × 5250/100
= 52500/100 = $525
Thus, simple interest for 1 year = $525
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $525 × 9 = $4725
Thus, Simple Interest (SI) = $4725
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $4725
= $9975
Thus, Amount to be paid = $9975 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?
(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.