Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $6880

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 = $6880 – $4300 = $2580

Thus, Simple Interest = $2580

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 × 2580}/_{4300 × 10}

= ²⁵⁸⁰⁰⁰/₄₃₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 10% per annum

Simple Interest = $2580 (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 = 10% of Principal

= 10% of $4300

= ¹⁰/₁₀₀ × 4300

= ^{10 × 4300}/₁₀₀

= ⁴³⁰⁰⁰/₁₀₀ = 430

Thus, simple Interest for 1 year = $430

Now,

∵ If the simple Interest is $430, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₀ years

∴ If the simple Interest is $2580, then the time = ¹/₄₃₀ × 2580 years

= ^{1 × 2580}/₄₃₀ years

= ²⁵⁸⁰/₄₃₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.

(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?

(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?

(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?

(7) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?

(9) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.