Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
Correct Answer
$8814
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5650 × 7% × 8
= $5650 ×7/100 × 8
= 5650 × 7 × 8/100
= 39550 × 8/100
= 316400/100
= $3164
Thus, Simple Interest = $3164
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 = $5650 + $3164
= $8814
Thus, Amount to be paid = $8814 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 = $5650
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 7% × 8)
= $5650 + ($5650 ×7/100 × 8)
= $5650 + (5650 × 7 × 8/100)
= $5650 + (39550 × 8/100)
= $5650 + (316400/100)
= $5650 + $3164 = $8814
Thus, Amount (A) to be paid = $8814 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5650, the simple interest in 1 year
= 7/100 × 5650
= 7 × 5650/100
= 39550/100 = $395.5
Thus, simple interest for 1 year = $395.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $395.5 × 8 = $3164
Thus, Simple Interest (SI) = $3164
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3164
= $8814
Thus, Amount to be paid = $8814 Answer
Similar Questions
(1) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.