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) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(2) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(3) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.

(8) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

(9) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.