Simple Interest
Math MCQs

Question :    Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5247

Rate of Simple Interest (R) = 2%

Time (T) = 3 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

$5247 = P (1 + 2% × 3)

⇒ $5247 = P (1 + ²/₁₀₀ × 3)

⇒ $5247 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $5247 = P (1 + ⁶/₁₀₀)

⇒ $5247 = P (^{100 + 6}/₁₀₀)

⇒ $5247 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $5247

⇒ P = ⁵²⁴⁷/_¹⁰⁶/100

⇒ P = 5247 × ¹⁰⁰/₁₀₆

⇒ P = ^{5247 × 100}/₁₀₆

⇒ P = ⁵²⁴⁷⁰⁰/₁₀₆

⇒ P = $4950

Thus, the sum borrowed (P) = $4950 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 5247, then the Principal = ¹⁰⁰/₁₀₆ × 5247

= ^{100 × 5247}/₁₀₆

= ⁵²⁴⁷⁰⁰/₁₀₆

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.

(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(4) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?

(6) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?

(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?

(9) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.