Finance question

Question

You want $1,000 in 4 years. Your father will give you $400 one year from now (year 1) to help you out. In addition to your father's money, you plan to make payments every 6 months at 8% until you reach your goal. What is the amount of these payments? Identify the TVM problem types and show your w

Answer 1

This problem implies that 8% interest is compounded semi-annually. A diagram helps you to see that is taking place, what you have, and what you need to solve. So we'll se 2 periods before your father gives you money, and 8 periods total

 

----P----P+$400----P--  ---P----P---P PV=$1,000

 

What you have to find is the size of the semi-annual payment you will make so that the total ends up at $1,000

 

First we can find to what amount will your father's payment grow. It will grow for 6 periods

 

FV = $400 * (1 + .04)^6 = 506.13

 

So the future value of what you have to invest is $1,000 - 506.13 = $493.87

 

Solve for the rent (PMT) of an ordinary annuity whose future value = $493.87. Solving the formula can be tedious but a financial calculator or a spreadsheet function makes this simple.

 

 

FV = 493.87

N = 8

i% = 4%

PV = 0

PMT = ?

 

Your monthly payment should be $51.54, including the period when your father gives you $400.