A bank offers following 4 schemes for investment. If a customer wants to invest an amount of Rs. P, then which scheme is more beneficial for a customer after a period of 1 year I. Rate of invest 24% per annum compounded quarterly II. Rate of interest 24% per annum compounded half-yearly III. Rate of interest 24% per annum compounded annually IV. Rate of interest 24% per annum with simple interest ?

Question

A bank offers following 4 schemes for investment. If a customer wants to invest an amount of Rs. P, then which scheme is more beneficial for a customer after a period of 1 year I. Rate of invest 24% per annum compounded quarterly II. Rate of interest 24% per annum compounded half-yearly III. Rate of interest 24% per annum compounded annually IV. Rate of interest 24% per annum with simple interest ?

III
IV
II
I

LohaHridoy

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2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 4 : I

Given:

Principal = P, time =1 year, rate of interest = 24%

Formula used:

when interest is compounded annually

A = P(1 + r%)^t

where A, P, r and t are amount, principal, rate and time respectively.

When interest is simple interest.

Simple interest = (P × r × t)/100

Calculation:

When compound is quartely, then rate is divided by 4 and time is multiply by 4

A = 100(1 + 6%)⁴

⇒ A = 100 ( 1 + 0.06)⁴

⇒ A = 100 (1.06)⁴

⇒ A = 100 × 1.262

⇒ A = 126

when interest is half yearly, then rate is divided by 2 and time is multiply by 2.

A = 100 (1 + 12%)²

⇒ A = 100 ( 1 + 0.12)²

⇒ A = 100 × 1.12

⇒ A = 100 × 1.2544

⇒ A = 125.44

when interest is annually.

A = 100 (1 + 24%)¹

⇒ A = 100 (1 + 0.24)

⇒ A = 100 × 1.24

⇒ A = 124

simple interest = (100 × 24 × 1)/100

⇒ 24

Amount = 100 + 24

⇒ Rs. 124

In all the above cases, amount is maximum when compound is quartely.

∴ scheme I is more beneficial for a customer after a period of 1 year.