Simple Interest
Math MCQs

Question :    In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3200

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

Amount (A) = $3840

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 = $3840 – $3200 = $640

Thus, Simple Interest = $640

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 × 640}/_{3200 × 4}

= ⁶⁴⁰⁰⁰/₁₂₈₀₀

= 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) = $3200

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

Simple Interest = $640 (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 $3200

= ⁴/₁₀₀ × 3200

= ^{4 × 3200}/₁₀₀

= ¹²⁸⁰⁰/₁₀₀ = 128

Thus, simple Interest for 1 year = $128

Now,

∵ If the simple Interest is $128, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₈ years

∴ If the simple Interest is $640, then the time = ¹/₁₂₈ × 640 years

= ^{1 × 640}/₁₂₈ years

= ⁶⁴⁰/₁₂₈ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

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

(2) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.

(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.

(7) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.

(10) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.