Question

1)The current cost of graduate school tuition is $15,000 per year.
The cost of tuition is rising at 6.00% per year.
You plan to attend graduate school for 2 years starting 2 years from now.

How much do you have to invest today if your savings account earns 3.00% APR compounded annually to just fund your tuition?

Group of answer choices

A) $31,323

B) $32,754

C) $32,236

D) $30,437

2) You would like to purchase a vacation home in 6 years.
The current price of such a home is $500,000 but the price of these types of homes is rising at a rate of 3% per year.
How much would you have to invest today in nominal terms to exactly pay for the vacation home if your investments earn 5% APR (compounded annually) in nominal terms?

Group of answer choices

A) $445,510

B) $461,548

C) $373,108

D) $597,026

Answer 1

1. In this case we need to compute the present value which are computed as follows:

Cost of tuition after 2 years

= $ 15,000 (1.06)²

= $ 16,854

This will be the school fees for 1st year

Present value of the above amount

= $ 16,854 / 1.03²
= $ 15,886.51 Approximately

Cost of tuition after 3 years

= $ 15,000 (1.06)³

= $ 17,865.24

This will be the school fees for 2nd year

Present value of the above amount

= $ 17,865.24 / 1.03³

= $ 16,349.23 Approximately

So we have to invest today amount of

= $ 15,886.51 + $ 16,349.23

= $ 32,235.74 Approximately

So the correct answer is option c i.e. $ 32,236.

2. Amount that we have to invest today in nominal terms to exactly pay for the vacation home is computed as shown below:

Future value of home after 6 years

= $ 500,000 (1.03)⁶

= $ 597,026.1483

Present value of home at discount rate of 5%

= $ 597,026.1483 / 1.05⁶

= $ 445,510 Approximately

So the correct answer is option a i.e. $ 445,510

Feel free to ask in case of any query relating to this question