Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6396

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 = $6396 – $4100 = $2296

Thus, Simple Interest = $2296

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 × 2296}/_{4100 × 8}

= ²²⁹⁶⁰⁰/₃₂₈₀₀

= 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) = $4100

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

Simple Interest = $2296 (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 $4100

= ⁸/₁₀₀ × 4100

= ^{8 × 4100}/₁₀₀

= ³²⁸⁰⁰/₁₀₀ = 328

Thus, simple Interest for 1 year = $328

Now,

∵ If the simple Interest is $328, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₈ years

∴ If the simple Interest is $2296, then the time = ¹/₃₂₈ × 2296 years

= ^{1 × 2296}/₃₂₈ years

= ²²⁹⁶/₃₂₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?

(2) 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.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.

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

(5) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?

(9) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?