Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7360

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 = $7360 – $4600 = $2760

Thus, Simple Interest = $2760

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 × 2760}/_{4600 × 6}

= ²⁷⁶⁰⁰⁰/₂₇₆₀₀

= 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) = $4600

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2760 (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 = 6% of Principal

= 6% of $4600

= ⁶/₁₀₀ × 4600

= ^{6 × 4600}/₁₀₀

= ²⁷⁶⁰⁰/₁₀₀ = 276

Thus, simple Interest for 1 year = $276

Now,

∵ If the simple Interest is $276, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₇₆ years

∴ If the simple Interest is $2760, then the time = ¹/₂₇₆ × 2760 years

= ^{1 × 2760}/₂₇₆ years

= ²⁷⁶⁰/₂₇₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.

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

(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(5) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(7) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?

(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

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