Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 8% 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  8

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 8% 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 – $4000 = $2560

Thus, Simple Interest = $2560

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 × 2560}/_{4000 × 8}

= ²⁵⁶⁰⁰⁰/₃₂₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 8% per annum

Simple Interest = $2560 (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 = 8% of Principal

= 8% of $4000

= ⁸/₁₀₀ × 4000

= ^{8 × 4000}/₁₀₀

= ³²⁰⁰⁰/₁₀₀ = 320

Thus, simple Interest for 1 year = $320

Now,

∵ If the simple Interest is $320, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₀ years

∴ If the simple Interest is $2560, then the time = ¹/₃₂₀ × 2560 years

= ^{1 × 2560}/₃₂₀ years

= ²⁵⁶⁰/₃₂₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?

(2) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

(3) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?

(5) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.

(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(10) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.