Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
Correct Answer
$10170
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5650 ×10/100 × 8
= 5650 × 10 × 8/100
= 56500 × 8/100
= 452000/100
= $4520
Thus, Simple Interest = $4520
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 + $4520
= $10170
Thus, Amount to be paid = $10170 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 10% × 8)
= $5650 + ($5650 ×10/100 × 8)
= $5650 + (5650 × 10 × 8/100)
= $5650 + (56500 × 8/100)
= $5650 + (452000/100)
= $5650 + $4520 = $10170
Thus, Amount (A) to be paid = $10170 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5650, the simple interest in 1 year
= 10/100 × 5650
= 10 × 5650/100
= 56500/100 = $565
Thus, simple interest for 1 year = $565
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $565 × 8 = $4520
Thus, Simple Interest (SI) = $4520
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $4520
= $10170
Thus, Amount to be paid = $10170 Answer
Similar Questions
(1) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.
(8) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.
(10) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.