Question:
Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
Correct Answer
$9209.5
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 7%
Time (t) = 9 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% × 9
= $5650 ×7/100 × 9
= 5650 × 7 × 9/100
= 39550 × 9/100
= 355950/100
= $3559.5
Thus, Simple Interest = $3559.5
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 + $3559.5
= $9209.5
Thus, Amount to be paid = $9209.5 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) = 9 years
Thus, Amount (A)
= $5650 + ($5650 × 7% × 9)
= $5650 + ($5650 ×7/100 × 9)
= $5650 + (5650 × 7 × 9/100)
= $5650 + (39550 × 9/100)
= $5650 + (355950/100)
= $5650 + $3559.5 = $9209.5
Thus, Amount (A) to be paid = $9209.5 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 9 years
= Simple interest for 1 year × 9
= $395.5 × 9 = $3559.5
Thus, Simple Interest (SI) = $3559.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3559.5
= $9209.5
Thus, Amount to be paid = $9209.5 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(2) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?
(3) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.