Simple Interest
Math MCQs

Question :    How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $7740

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

$7740 = P (1 + 4% × 5)

⇒ $7740 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7740 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7740 = P (1 + ²⁰/₁₀₀)

⇒ $7740 = P (^{100 + 20}/₁₀₀)

⇒ $7740 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7740

⇒ P = ⁷⁷⁴⁰/_¹²⁰/100

⇒ P = 7740 × ¹⁰⁰/₁₂₀

⇒ P = ^{7740 × 100}/₁₂₀

⇒ P = ⁷⁷⁴⁰⁰⁰/₁₂₀

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 7740, then the Principal = ¹⁰⁰/₁₂₀ × 7740

= ^{100 × 7740}/₁₂₀

= ⁷⁷⁴⁰⁰⁰/₁₂₀

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?

(4) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.

(6) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(7) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(8) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?

(10) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.