Bob and Jane Loveboat are saving to buy a boat at the end of 5 years.
If the boat
costs $25,000, and they can earn 8 percent a year on their savings, how much do
they need to put aside at the end of every year 1 through 5?
You need to find the amount they need to set aside every year such that the
annual savings, invested at 8 percent a year, accumulate to $25,000.
you have an annuity of $C with FV = $25,000.
Recall that the formula for
the future value of an annuity is given by:
where C is the annual payment, r is the annual year interest rate, FV is the
future value of the annuity.
Therefore we have:
Solving for C gives, C = $4,261.41
Leeds Autos has just announced its new promotional deal on the new $45,000 Z4
You pay $5,000 down, and then $1000 for the next 40 months.
door competitor, Chatham Hill Autos will give you a $3000 off the list price
If the interest rate is 6% a year, which company is giving a better
You need to compare the present value of the two streams of payments,
paying $42,000 today, vs. paying $5000 today, plus $1000 for the next 40
Note that the payments are monthly, so we need to use the monthly
rate of 6%/12 = 0.5%.
The present value of Leeds Autos offer:
$5000 + PV(annuity($1000,T=40,r=0.5%))