Question

1. Hector's parents anticipate needing $80,000 when he is 18 for his college education. a. [4 pts]If he is 5 years old now, how much should they invest in an investment plan that pays 6.23% compounded quarterly? b. [2 pts]Hector ended up getting a full scholarship. His parents agreed to let him draw the interest off the investment account each quarter (3 months) for expenses. How much will Hector receive each quarter? 2. Meagan invests $1,200 each year in an IRA for 12 years in an account that earned 5% compounded annually. At the end of 12 years, she stopped making payments to the account, but continued to invest her accumulated amount at 5% compounded annually for the next 11 years. a. [4 pts] What was the value of the IRA at the end of 12 years? b. [3 pt] What was the value of the investment at the end of the next 11 years? 3. Suppose Miss Roxanne Davenport is 25 years old right now and puts away $1,800 per quarter in an account that returns 6% interest. a. [4 pts] How much will be in the account when she turns 65? b. [1 pt] What is her total contribution to the account? C. [2 pts] How much interest did she earn?

Answer 1

1.a.

We can use the present value (PV) formula here,

FV PV (1 i/a)na

Where,

PV = Present Value

FV = Future Value

n = number periods (18 - 5 = 13 years)

i = rate of return or interest.

a = frequency of compounding ( 4 in case of quarterly)

So let us put the values in the formula:

$PV = \frac{80000}{(1+0.0623/4)^{13*4}}$

$PV = \frac{80000}{2.233696}$

So they must invest $35,815 now.

1.b

At the age of 18 he has $80,000 in his account.

Interest per quarter :

$= 80000 *\frac{0.0623}{4}$

Therefore, he can withdraw $1,246 per quarter.

2.a. We can use future value of annuity (FVA) formula here,

$FVA = A\left [ \frac{(1+i)^n-1}{i}\right ]$

Where, A = Annuity / Investment each year.

$FVA = 1200\left [ \frac{(1+0.05)^{12}-1}{0.05}\right ]$

$= 1200\left [15.917127 ]$

$=19100.55$

Therefore, the value of IRA at the end of 12 years is $19,100.55

2.b

She stopped making payments after 12 years but the account compounded annually for next 11 years. The value of investment at the end of next 11 years can be determined by using the formula for future value (FV).

Here PV = Principal amount or present value of investment.

Therefore at the end of next 11 years the value of investment will be $32,668.42