Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
Correct Answer
$7068
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 3%
Time (t) = 8 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% × 8
= $5700 ×3/100 × 8
= 5700 × 3 × 8/100
= 17100 × 8/100
= 136800/100
= $1368
Thus, Simple Interest = $1368
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 + $1368
= $7068
Thus, Amount to be paid = $7068 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) = 8 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 8)
= $5700 + ($5700 ×3/100 × 8)
= $5700 + (5700 × 3 × 8/100)
= $5700 + (17100 × 8/100)
= $5700 + (136800/100)
= $5700 + $1368 = $7068
Thus, Amount (A) to be paid = $7068 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 8 years
= Simple interest for 1 year × 8
= $171 × 8 = $1368
Thus, Simple Interest (SI) = $1368
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1368
= $7068
Thus, Amount to be paid = $7068 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.