Simple Interest
Math MCQs

Question :    How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?

Correct Answer  $5850

Solution & Explanation

Solution

Given,

Amount (A) = $7020

Rate of Simple Interest (R) = 4%

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

$7020 = P (1 + 4% × 5)

⇒ $7020 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7020 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7020 = P (1 + ²⁰/₁₀₀)

⇒ $7020 = P (^{100 + 20}/₁₀₀)

⇒ $7020 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7020

⇒ P = ⁷⁰²⁰/_¹²⁰/100

⇒ P = 7020 × ¹⁰⁰/₁₂₀

⇒ P = ^{7020 × 100}/₁₂₀

⇒ P = ⁷⁰²⁰⁰⁰/₁₂₀

⇒ P = $5850

Thus, the sum borrowed (P) = $5850 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7020, then the Principal = ¹⁰⁰/₁₂₀ × 7020

= ^{100 × 7020}/₁₂₀

= ⁷⁰²⁰⁰⁰/₁₂₀

= 5850

Thus, Principal = $5850

Thus, the sum borrowed = $5850 Answer

Similar Questions

(1) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?

(2) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(4) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(6) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?

(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?

(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?

(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.