Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

Correct Answer  $8965

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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) = $5500 × 7% × 9

= $5500 ×⁷/₁₀₀ × 9

= ^{5500 × 7 × 9}/₁₀₀

= ^{38500 × 9}/₁₀₀

= ³⁴⁶⁵⁰⁰/₁₀₀

= $3465

Thus, Simple Interest = $3465

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 = $5500 + $3465

= $8965

Thus, Amount to be paid = $8965 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 = $5500

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5500 + ($5500 × 7% × 9)

= $5500 + ($5500 ×⁷/₁₀₀ × 9)

= $5500 + (^{5500 × 7 × 9}/₁₀₀)

= $5500 + (^{38500 × 9}/₁₀₀)

= $5500 + (³⁴⁶⁵⁰⁰/₁₀₀)

= $5500 + $3465 = $8965

Thus, Amount (A) to be paid = $8965 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 $5500, the simple interest in 1 year

= ⁷/₁₀₀ × 5500

= ^{7 × 5500}/₁₀₀

= ³⁸⁵⁰⁰/₁₀₀ = $385

Thus, simple interest for 1 year = $385

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $385 × 9 = $3465

Thus, Simple Interest (SI) = $3465

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $3465

= $8965

Thus, Amount to be paid = $8965 Answer

Similar Questions

(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.

(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.

(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(8) 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.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.

(10) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.