Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4800

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

Amount (A) = $7392

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 = $7392 – $4800 = $2592

Thus, Simple Interest = $2592

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 × 2592}/_{4800 × 9}

= ²⁵⁹²⁰⁰/₄₃₂₀₀

= 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) = $4800

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

Simple Interest = $2592 (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 $4800

= ⁹/₁₀₀ × 4800

= ^{9 × 4800}/₁₀₀

= ⁴³²⁰⁰/₁₀₀ = 432

Thus, simple Interest for 1 year = $432

Now,

∵ If the simple Interest is $432, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₂ years

∴ If the simple Interest is $2592, then the time = ¹/₄₃₂ × 2592 years

= ^{1 × 2592}/₄₃₂ years

= ²⁵⁹²/₄₃₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.

(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.

(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(9) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.