Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9720

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 = $9720 – $5400 = $4320

Thus, Simple Interest = $4320

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 × 4320}/_{5400 × 8}

= ⁴³²⁰⁰⁰/₄₃₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5400

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $4320 (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 = 8% of Principal

= 8% of $5400

= ⁸/₁₀₀ × 5400

= ^{8 × 5400}/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 $4320, then the time = ¹/₄₃₂ × 4320 years

= ^{1 × 4320}/₄₃₂ years

= ⁴³²⁰/₄₃₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(2) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.

(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?

(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?

(8) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.