Question

Samantha opened a savings account this morning. Her money will earn 5 percent interest, compounded annually.After five years, her savings account will be worth $5,600. Assume she will not make any withdrawals.Given this, which one of the following statements is true?a. Samantha deposited more than $5,600 this morning.b. Samantha could have deposited less money and still had $5,600 in five years if she could have earned 5.5 percent interest.c. The present value of Samantha's account is $5,600.d. Samantha would have had to deposit more money to have $5,600 in five years if she could have earned 6 percent interest.e. Samantha will earn an equal amount of interest every year for the next five years.

Answer 1

Answer:

Samantha could have deposited less money and still had $5,600 in five years if she could have earned 5.5 percent interest

Explanation:

Giving the following information:

Her money will earn 5 percent interest, compounded annually. After five years, her savings account will be worth $5,600.

First, we will calculate the original deposit. Then, we will tackle each statement and find the true one.

PV= FV/(1+i)^n

PV= 5,600/ (1.05^5)= $4,387.75

a. Samantha deposited more than $5,600 this morning. False, we just prove that she deposit less than 5,600

b. Samantha could have deposited less money and still had $5,600 in five years if she could have earned 5.5 percent interest. True. The higher the interest rate, in the same period the higher the ending value or lower the present value.

c. The present value of Samantha's account is $5,600. False, the final value is $5,600.

d. Samantha would have had to deposit more money to have $5,600 in five years if she could have earned 6 percent interest. False, she would have to deposit less than $5,600

e. Samantha will earn an equal amount of interest every year for the next five years. False. Because interest gets capitalized, each year the interest earned is higher.