Simple Interest
Math MCQs

Question :    If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $3942

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$3942 = P (1 + 2% × 4)

⇒ $3942 = P (1 + ²/₁₀₀ × 4)

⇒ $3942 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3942 = P (1 + ⁸/₁₀₀)

⇒ $3942 = P (^{100 + 8}/₁₀₀)

⇒ $3942 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3942

⇒ P = ³⁹⁴²/_¹⁰⁸/100

⇒ P = 3942 × ¹⁰⁰/₁₀₈

⇒ P = ^{3942 × 100}/₁₀₈

⇒ P = ³⁹⁴²⁰⁰/₁₀₈

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 3942, then the Principal = ¹⁰⁰/₁₀₈ × 3942

= ^{100 × 3942}/₁₀₈

= ³⁹⁴²⁰⁰/₁₀₈

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?

(2) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(5) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?

(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?