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) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(5) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(6) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(8) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?