Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

Correct Answer  $8755

Solution & Explanation

Solution

Given,

Principal (P) = $5150

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) = $5150 × 7% × 10

= $5150 ×⁷/₁₀₀ × 10

= ^{5150 × 7 × 10}/₁₀₀

= ^{36050 × 10}/₁₀₀

= ³⁶⁰⁵⁰⁰/₁₀₀

= $3605

Thus, Simple Interest = $3605

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 = $5150 + $3605

= $8755

Thus, Amount to be paid = $8755 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 = $5150

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 10 years

Thus, Amount (A)

= $5150 + ($5150 × 7% × 10)

= $5150 + ($5150 ×⁷/₁₀₀ × 10)

= $5150 + (^{5150 × 7 × 10}/₁₀₀)

= $5150 + (^{36050 × 10}/₁₀₀)

= $5150 + (³⁶⁰⁵⁰⁰/₁₀₀)

= $5150 + $3605 = $8755

Thus, Amount (A) to be paid = $8755 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 $5150, the simple interest in 1 year

= ⁷/₁₀₀ × 5150

= ^{7 × 5150}/₁₀₀

= ³⁶⁰⁵⁰/₁₀₀ = $360.5

Thus, simple interest for 1 year = $360.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $360.5 × 10 = $3605

Thus, Simple Interest (SI) = $3605

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $3605

= $8755

Thus, Amount to be paid = $8755 Answer

Similar Questions

(1) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?

(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(6) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

(7) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.

(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(10) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.