Question:
Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
Correct Answer
$7612.5
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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) = $5250 × 5% × 9
= $5250 ×5/100 × 9
= 5250 × 5 × 9/100
= 26250 × 9/100
= 236250/100
= $2362.5
Thus, Simple Interest = $2362.5
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 + $2362.5
= $7612.5
Thus, Amount to be paid = $7612.5 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5250 + ($5250 × 5% × 9)
= $5250 + ($5250 ×5/100 × 9)
= $5250 + (5250 × 5 × 9/100)
= $5250 + (26250 × 9/100)
= $5250 + (236250/100)
= $5250 + $2362.5 = $7612.5
Thus, Amount (A) to be paid = $7612.5 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 $5250, the simple interest in 1 year
= 5/100 × 5250
= 5 × 5250/100
= 26250/100 = $262.5
Thus, simple interest for 1 year = $262.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $262.5 × 9 = $2362.5
Thus, Simple Interest (SI) = $2362.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $2362.5
= $7612.5
Thus, Amount to be paid = $7612.5 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.
(2) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(5) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(8) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?