Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $9128

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 = $9128 – $5600 = $3528

Thus, Simple Interest = $3528

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 × 3528}/_{5600 × 9}

= ³⁵²⁸⁰⁰/₅₀₄₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $5600

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

Simple Interest = $3528 (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 $5600

= ⁹/₁₀₀ × 5600

= ^{9 × 5600}/₁₀₀

= ⁵⁰⁴⁰⁰/₁₀₀ = 504

Thus, simple Interest for 1 year = $504

Now,

∵ If the simple Interest is $504, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₄ years

∴ If the simple Interest is $3528, then the time = ¹/₅₀₄ × 3528 years

= ^{1 × 3528}/₅₀₄ years

= ³⁵²⁸/₅₀₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?

(5) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

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

(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(10) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.