Question:
Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
Correct Answer
$8585
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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% × 10
= $5050 ×7/100 × 10
= 5050 × 7 × 10/100
= 35350 × 10/100
= 353500/100
= $3535
Thus, Simple Interest = $3535
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 + $3535
= $8585
Thus, Amount to be paid = $8585 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) = 10 years
Thus, Amount (A)
= $5050 + ($5050 × 7% × 10)
= $5050 + ($5050 ×7/100 × 10)
= $5050 + (5050 × 7 × 10/100)
= $5050 + (35350 × 10/100)
= $5050 + (353500/100)
= $5050 + $3535 = $8585
Thus, Amount (A) to be paid = $8585 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 10 years
= Simple interest for 1 year × 10
= $353.5 × 10 = $3535
Thus, Simple Interest (SI) = $3535
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $3535
= $8585
Thus, Amount to be paid = $8585 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(10) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.