Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3596

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 = $3596 – $3100 = $496

Thus, Simple Interest = $496

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 × 496}/_{3100 × 4}

= ⁴⁹⁶⁰⁰/₁₂₄₀₀

= 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) = 4% per annum

Simple Interest = $496 (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 = 4% of Principal

= 4% of $3100

= ⁴/₁₀₀ × 3100

= ^{4 × 3100}/₁₀₀

= ¹²⁴⁰⁰/₁₀₀ = 124

Thus, simple Interest for 1 year = $124

Now,

∵ If the simple Interest is $124, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₄ years

∴ If the simple Interest is $496, then the time = ¹/₁₂₄ × 496 years

= ^{1 × 496}/₁₂₄ years

= ⁴⁹⁶/₁₂₄ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?

(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?

(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?

(9) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?