Simple Interest
Math MCQs

Question :    How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?

Correct Answer  $6950

Solution & Explanation

Solution

Given,

Amount (A) = $7645

Rate of Simple Interest (R) = 2%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$7645 = P (1 + 2% × 5)

⇒ $7645 = P (1 + ²/₁₀₀ × 5)

⇒ $7645 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7645 = P (1 + ¹⁰/₁₀₀)

⇒ $7645 = P (^{100 + 10}/₁₀₀)

⇒ $7645 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7645

⇒ P = ⁷⁶⁴⁵/_¹¹⁰/100

⇒ P = 7645 × ¹⁰⁰/₁₁₀

⇒ P = ^{7645 × 100}/₁₁₀

⇒ P = ⁷⁶⁴⁵⁰⁰/₁₁₀

⇒ P = $6950

Thus, the sum borrowed (P) = $6950 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7645, then the Principal = ¹⁰⁰/₁₁₀ × 7645

= ^{100 × 7645}/₁₁₀

= ⁷⁶⁴⁵⁰⁰/₁₁₀

= 6950

Thus, Principal = $6950

Thus, the sum borrowed = $6950 Answer

Similar Questions

(1) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(3) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.

(4) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.

(6) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.