Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3472

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $3472 – $3100 = $372

Thus, Simple Interest = $372

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 372}/_{3100 × 3}

= ³⁷²⁰⁰/₉₃₀₀

= 4 years (using formula)

Thus, Time (T) = 4 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $3100

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $372 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 3% of Principal

= 3% of $3100

= ³/₁₀₀ × 3100

= ^{3 × 3100}/₁₀₀

= ⁹³⁰⁰/₁₀₀ = 93

Thus, simple Interest for 1 year = $93

Now,

∵ If the simple Interest is $93, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₃ years

∴ If the simple Interest is $372, then the time = ¹/₉₃ × 372 years

= ^{1 × 372}/₉₃ years

= ³⁷²/₉₃ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?

(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(4) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.

(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?