Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6683

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 = $6683 – $4100 = $2583

Thus, Simple Interest = $2583

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 × 2583}/_{4100 × 7}

= ²⁵⁸³⁰⁰/₂₈₇₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 7% per annum

Simple Interest = $2583 (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 = 7% of Principal

= 7% of $4100

= ⁷/₁₀₀ × 4100

= ^{7 × 4100}/₁₀₀

= ²⁸⁷⁰⁰/₁₀₀ = 287

Thus, simple Interest for 1 year = $287

Now,

∵ If the simple Interest is $287, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₇ years

∴ If the simple Interest is $2583, then the time = ¹/₂₈₇ × 2583 years

= ^{1 × 2583}/₂₈₇ years

= ²⁵⁸³/₂₈₇ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.

(7) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.