Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $5960

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 = $5960 – $4000 = $1960

Thus, Simple Interest = $1960

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 × 1960}/_{4000 × 7}

= ¹⁹⁶⁰⁰⁰/₂₈₀₀₀

= 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) = $4000

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

Simple Interest = $1960 (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 $4000

= ⁷/₁₀₀ × 4000

= ^{7 × 4000}/₁₀₀

= ²⁸⁰⁰⁰/₁₀₀ = 280

Thus, simple Interest for 1 year = $280

Now,

∵ If the simple Interest is $280, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₀ years

∴ If the simple Interest is $1960, then the time = ¹/₂₈₀ × 1960 years

= ^{1 × 1960}/₂₈₀ years

= ¹⁹⁶⁰/₂₈₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.

(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(6) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

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

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.

(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.