Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6560

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 = $6560 – $4100 = $2460

Thus, Simple Interest = $2460

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 × 2460}/_{4100 × 6}

= ²⁴⁶⁰⁰⁰/₂₄₆₀₀

= 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) = $4100

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

Simple Interest = $2460 (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 $4100

= ⁶/₁₀₀ × 4100

= ^{6 × 4100}/₁₀₀

= ²⁴⁶⁰⁰/₁₀₀ = 246

Thus, simple Interest for 1 year = $246

Now,

∵ If the simple Interest is $246, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₆ years

∴ If the simple Interest is $2460, then the time = ¹/₂₄₆ × 2460 years

= ^{1 × 2460}/₂₄₆ years

= ²⁴⁶⁰/₂₄₆ = 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 7% simple interest?

(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.

(4) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.

(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?

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