Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $7009

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 = $7009 – $4300 = $2709

Thus, Simple Interest = $2709

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 × 2709}/_{4300 × 7}

= ²⁷⁰⁹⁰⁰/₃₀₁₀₀

= 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) = $4300

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

Simple Interest = $2709 (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 $4300

= ⁷/₁₀₀ × 4300

= ^{7 × 4300}/₁₀₀

= ³⁰¹⁰⁰/₁₀₀ = 301

Thus, simple Interest for 1 year = $301

Now,

∵ If the simple Interest is $301, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₁ years

∴ If the simple Interest is $2709, then the time = ¹/₃₀₁ × 2709 years

= ^{1 × 2709}/₃₀₁ years

= ²⁷⁰⁹/₃₀₁ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?

(2) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(4) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.

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

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(9) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?