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 $6800 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $6800

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 = $6800 – $4000 = $2800

Thus, Simple Interest = $2800

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 × 2800}/_{4000 × 7}

= ²⁸⁰⁰⁰⁰/₂₈₀₀₀

= 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) = $4000

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

Simple Interest = $2800 (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 $2800, then the time = ¹/₂₈₀ × 2800 years

= ^{1 × 2800}/₂₈₀ years

= ²⁸⁰⁰/₂₈₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?

(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?

(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?

(4) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?

(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?