Question:
Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
Correct Answer
$8231.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 7% × 9
= $5050 ×7/100 × 9
= 5050 × 7 × 9/100
= 35350 × 9/100
= 318150/100
= $3181.5
Thus, Simple Interest = $3181.5
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 = $5050 + $3181.5
= $8231.5
Thus, Amount to be paid = $8231.5 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 = $5050
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5050 + ($5050 × 7% × 9)
= $5050 + ($5050 ×7/100 × 9)
= $5050 + (5050 × 7 × 9/100)
= $5050 + (35350 × 9/100)
= $5050 + (318150/100)
= $5050 + $3181.5 = $8231.5
Thus, Amount (A) to be paid = $8231.5 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 $5050, the simple interest in 1 year
= 7/100 × 5050
= 7 × 5050/100
= 35350/100 = $353.5
Thus, simple interest for 1 year = $353.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $353.5 × 9 = $3181.5
Thus, Simple Interest (SI) = $3181.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3181.5
= $8231.5
Thus, Amount to be paid = $8231.5 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(3) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(7) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?
(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?