Simple Interest
Math MCQs

Question :    How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?

Correct Answer  $6850

Solution & Explanation

Solution

Given,

Amount (A) = $7535

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

$7535 = P (1 + 2% × 5)

⇒ $7535 = P (1 + ²/₁₀₀ × 5)

⇒ $7535 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7535 = P (1 + ¹⁰/₁₀₀)

⇒ $7535 = P (^{100 + 10}/₁₀₀)

⇒ $7535 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7535

⇒ P = ⁷⁵³⁵/_¹¹⁰/100

⇒ P = 7535 × ¹⁰⁰/₁₁₀

⇒ P = ^{7535 × 100}/₁₁₀

⇒ P = ⁷⁵³⁵⁰⁰/₁₁₀

⇒ P = $6850

Thus, the sum borrowed (P) = $6850 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 7535, then the Principal = ¹⁰⁰/₁₁₀ × 7535

= ^{100 × 7535}/₁₁₀

= ⁷⁵³⁵⁰⁰/₁₁₀

= 6850

Thus, Principal = $6850

Thus, the sum borrowed = $6850 Answer

Similar Questions

(1) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?

(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?

(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(6) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(8) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.

(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(10) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?