Question

Suppose Jennifer deposits $500 in an account at the end of this year, $400 at the end of the next year, and $300 at the end of the followin g year. If her opportunity cost rate is 7.5 percent, how much will be in the account immediately after the third deposit is made? How m uch will be in the account at the end of three years if t he deposits are made at the beginning of each year?

Answer 1

Step-by-step explanation:

Formula required to find remaining amount in account:

A = P ( 1 + r / 100 )^n

Here

A represents future value

P represents present value

r represents rate of interest

n represents time period.

a)

As Jennifer deposits $500 in an account at the end of this year, $400 at the end of the next year, and $300 at the end of the following year.

Therefore by putting the values in the above formula, we get

At the end of 3 years:

A = 500 * (1 + 7.5 / 100)^2

A = 500 * (1.075)^2

At the end of next year:

A = 400 * (1 + 7.5 / 100)

A = 400 * (1.075)

At the end of following year:

A = 300

Adding all these together, we get

A = 500 * (1.075)^2 + 400 * (1.075) + 300

A = $1307.8125

b)

At the end of 3 years:

A = 500 * (1 + 7.5 / 100)^3

A = 500 * (1.075)^3

At the end of next year:

A = 400 * (1 + 7.5 / 100)^2

A = 400 * (1.075)^2

At the end of following year:

A = 300*(1.075)

Adding all these together, we get

A = 500*(1.075)^3+400*(1.075)^2+300*(1.075)

A = $1405.90