Question:
Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
Correct Answer
$7239
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5700 × 3% × 9
= $5700 ×3/100 × 9
= 5700 × 3 × 9/100
= 17100 × 9/100
= 153900/100
= $1539
Thus, Simple Interest = $1539
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 = $5700 + $1539
= $7239
Thus, Amount to be paid = $7239 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 = $5700
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 9)
= $5700 + ($5700 ×3/100 × 9)
= $5700 + (5700 × 3 × 9/100)
= $5700 + (17100 × 9/100)
= $5700 + (153900/100)
= $5700 + $1539 = $7239
Thus, Amount (A) to be paid = $7239 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5700, the simple interest in 1 year
= 3/100 × 5700
= 3 × 5700/100
= 17100/100 = $171
Thus, simple interest for 1 year = $171
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $171 × 9 = $1539
Thus, Simple Interest (SI) = $1539
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1539
= $7239
Thus, Amount to be paid = $7239 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(4) 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.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.