Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3875

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 = $3875 – $3100 = $775

Thus, Simple Interest = $775

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 × 775}/_{3100 × 5}

= ⁷⁷⁵⁰⁰/₁₅₅₀₀

= 5 years (using formula)

Thus, Time (T) = 5 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) = 5% per annum

Simple Interest = $775 (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 = 5% of Principal

= 5% of $3100

= ⁵/₁₀₀ × 3100

= ^{5 × 3100}/₁₀₀

= ¹⁵⁵⁰⁰/₁₀₀ = 155

Thus, simple Interest for 1 year = $155

Now,

∵ If the simple Interest is $155, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₅₅ years

∴ If the simple Interest is $775, then the time = ¹/₁₅₅ × 775 years

= ^{1 × 775}/₁₅₅ years

= ⁷⁷⁵/₁₅₅ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?

(3) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.

(9) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(10) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.