Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9856

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 = $9856 – $6400 = $3456

Thus, Simple Interest = $3456

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 × 3456}/_{6400 × 9}

= ³⁴⁵⁶⁰⁰/₅₇₆₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $6400

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3456 (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 = 9% of Principal

= 9% of $6400

= ⁹/₁₀₀ × 6400

= ^{9 × 6400}/₁₀₀

= ⁵⁷⁶⁰⁰/₁₀₀ = 576

Thus, simple Interest for 1 year = $576

Now,

∵ If the simple Interest is $576, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₇₆ years

∴ If the simple Interest is $3456, then the time = ¹/₅₇₆ × 3456 years

= ^{1 × 3456}/₅₇₆ years

= ³⁴⁵⁶/₅₇₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(2) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.

(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(7) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.