Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
Correct Answer
$9676
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5900 × 8% × 8
= $5900 ×8/100 × 8
= 5900 × 8 × 8/100
= 47200 × 8/100
= 377600/100
= $3776
Thus, Simple Interest = $3776
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 = $5900 + $3776
= $9676
Thus, Amount to be paid = $9676 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 = $5900
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5900 + ($5900 × 8% × 8)
= $5900 + ($5900 ×8/100 × 8)
= $5900 + (5900 × 8 × 8/100)
= $5900 + (47200 × 8/100)
= $5900 + (377600/100)
= $5900 + $3776 = $9676
Thus, Amount (A) to be paid = $9676 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5900, the simple interest in 1 year
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = $472
Thus, simple interest for 1 year = $472
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $472 × 8 = $3776
Thus, Simple Interest (SI) = $3776
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $3776
= $9676
Thus, Amount to be paid = $9676 Answer
Similar Questions
(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?
(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?
(6) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?
(8) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?