Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3050

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

Amount (A) = $3416

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 = $3416 – $3050 = $366

Thus, Simple Interest = $366

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 × 366}/_{3050 × 4}

= ³⁶⁶⁰⁰/₁₂₂₀₀

= 3 years (using formula)

Thus, Time (T) = 3 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) = $3050

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

Simple Interest = $366 (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 $3050

= ⁴/₁₀₀ × 3050

= ^{4 × 3050}/₁₀₀

= ¹²²⁰⁰/₁₀₀ = 122

Thus, simple Interest for 1 year = $122

Now,

∵ If the simple Interest is $122, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₂ years

∴ If the simple Interest is $366, then the time = ¹/₁₂₂ × 366 years

= ^{1 × 366}/₁₂₂ years

= ³⁶⁶/₁₂₂ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

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

(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?

(3) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.

(5) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.

(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.