Question

Calculate the following time value of money problems.

a) What is the future value of 20 periodic payments of $4,620 each made at the beginningof each period and compounded at 6% per period?

b) What would you pay for a $300,000 face value bond that matures in 15 years and pays $35,000 a year in interest (end-of-period payments) if you wanted to earn a yield of 9%.

c) Mike Finley wishes to become a millionaire. His money market fund has a balance of $555,264.50 and has a guaranteed interest rate of 4%. How many years must Mike leave that balance in the fund in order to get his desired $1,000,000?

d) Andrew Bogut just received a signing bonus of $1,000,000. His plan is to invest this payment in a fund for 8 years (his planned retirement date).  If Bogut plans to establish the AB Foundation once the fund grows to $1,850,930, what annually compoundedinterest rate must he earn to achieve his goal?

Answer 1

Solution a:

Future value = $4,620 * Cumulative FV fact at 6% for 20 periods of annuity due

= $4,620 * 38.99273

= $180,146.

Solution b:

Computation of bond price
Table values are based on:
n=	15
i=	9%
Cash flow	Table Value	Amount	Present Value
Par (Maturity) Value	0.27454	$300,000	$82,361
Interest (Annuity)	8.06069	$35,000	$282,124
Price of bonds			$364,486

Solution c:

Balance in fund = $555,264.50

Future value = $1,000,000

Interest rate = 4%

Lets time period = n

Now

$555,264.50 * (1+0.04) ^n = $1,000,000

(1.04)^n = 1.80094

Refer CI Table, n = 15 Years

Solution d:

Investment amount = $1,000,000

Future value = $1,850,930

Period = 8 year

Let interest rate is i

Noew

$1,000,000 * (1+i)^8 = $1,850,930

(1+i)^8 = 1.85093

Refer CI table, i = 8%