Question

The same amount of principal is invested in different accounts earning the same interest rate. Which of the following accounts would have the greatest accumulated value at the end of one year?
a. An account earning no interest
b. An account earning simple interest
c. An account earning interest compounded annually
d. An account earning interest compounded daily

Answer 1

D.) An account earning interest compounded daily.

This is the account that would have the greatest accumulated value at the end of one year.

Let us assume the following figures.
Principal = 1,000
Interest rate = 12% p.a.
Term 1 year 

a) account earning no interest = 1,000
b) account earning simple interest
S.I. = 1,000 x 12% x 1 = 120 
Balance = 1000 + 120= 1,120
c) account earning interest compounded annually
FV = 1,000 (1+.12)¹
FV = 1,000 (1.12)
FV = 1,120
d) account compounded daily
FV = 1,000 (1 + .12/365)³⁶⁵
FV = 1,000 (1 + 0.00033)³⁶⁵
FV = 1,000 (1.00033)³⁶⁵
FV = 1,000 (1.128)
FV = 1,128

Answer 2

Option (d) is correct.

An account that earns the interest compounded daily would have the greatest accumulated value at the end of one year.

Further Explanation:

Compound interest:  Compound interest is a type of interest where the interest is calculated on the principle and the earned interest. Generally, the principle is considered in the calculation of the interest (simple interest). The compound interest is calculated on the principal amount and the earned interest amount. So, the interest tends to increase because of the compounding nature. Compounding means the ability to earn from prior earnings. So, compound interest earns the interest from the already earned interest in the prior year. It is considered as “interest on interest”.

Rate of compound interest:  The amount of compound interest increases with the increase in the frequency rate. The frequency rate is the rate of compounding the interest. The interest value will be higher when the interest is calculated or compounded more frequently. The amount of interest will be higher in case of a higher number of the compounding period.

In the current case, the interest will be higher in case of daily compounding as the frequency of compounding will be 365 times rather than 1 in case of annual compounding. Compound interest always results in a higher amount of interest than simple interest because of the compounding factor.

Thus, the account that earns the interest compounded daily would have the greatest accumulated value at the end of one year.

a.

An account earning no interest: This is an incorrect option.

There will be no interest, so it cannot have the highest accumulated value at the end of the year.

b.

An account earning simple interest: This is an incorrect option.

Simple interest results in lower interest amount than compound interest.

c.

An account earning interest compounded annually: This is an incorrect option.

The frequency of annual compound is only 1 as compared to 365 in case of a daily compound.

d.

An account earning interest compounded daily: This is the correct option.

If the interest will be compounded daily; the frequency will be highest out of all the cases so it will result in the accumulated value.

Learn more:

Learn more about the account with high liquidity and no-interest bank account

brainly.com/question/2899952

Learn more about the interest on the bond

brainly.com/question/1442514

Learn more about the interest on the credit card

brainly.com/question/5993991  

Answer details:

Grade: High School

Subject: Business Studies

Chapter: Money & Banking

Keywords: Same amount, principal, invested, different accounts, earning, same interest rate, accounts, would,  greatest, accumulated, value, at the end of one year, simple interest, compound interest, daily, annually, no interest, account, bank account.