Question

The Nashville Geetars, a professional foosball team, has just signed its star player Harold "The Wrist" Thornton to a new contract. One of the terms requires the team to make a lump sum payment of $13.17 million to the The Wrist exactly 9 years from today. The team plans to make equal annual deposits into an account that will earn 4.84 percent in order to fund the payment. How much must the team deposit each year?

What is the effective annual rate for an APR of 15.50 percent compounded monthly?

Answer 1

First question:

Payment required	=		FV*r /[(1+r)^n -1]
Future value	FV		13,170,000.00
Rate per period	r
Annual interest			4.84%
Number of interest payments per year			1
Interest rate per period			0.0484/1=
Interest rate per period			4.840%
Number of periods	n
Number of years			9
Periods per year			1
number of periods			9
Period payment	=		13170000*0.0484/ [(1+0.0484)^9 -1]
	=		1,202,281.31

Annuity payment required is $1,202,281.31 per year for nine years.

Second question:

	Effective annual interest rate=	(1+periodic interest rate)^m   -1
rs=	Stated interest rate	4.84%
m	number of compoundings in a year	12
rs/m	period interest rate	0.4033333%
	Effective annual interest rate=	(1+0.004033)^12    -1
	Effective annual interest rate=	4.95%

Effective annual rate is 4.95%

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