Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
Correct Answer
$10735
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 10%
Time (t) = 9 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% × 9
= $5650 ×10/100 × 9
= 5650 × 10 × 9/100
= 56500 × 9/100
= 508500/100
= $5085
Thus, Simple Interest = $5085
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 + $5085
= $10735
Thus, Amount to be paid = $10735 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) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 10% × 9)
= $5650 + ($5650 ×10/100 × 9)
= $5650 + (5650 × 10 × 9/100)
= $5650 + (56500 × 9/100)
= $5650 + (508500/100)
= $5650 + $5085 = $10735
Thus, Amount (A) to be paid = $10735 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 9 years
= Simple interest for 1 year × 9
= $565 × 9 = $5085
Thus, Simple Interest (SI) = $5085
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $5085
= $10735
Thus, Amount to be paid = $10735 Answer
Similar Questions
(1) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(3) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(5) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 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 2% simple interest.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.