Determining Unknown Quantities Determine the unknown quantit

Determining Unknown Quantities Determine the unknown quantity for each of the following independent situations using the appropriate interest tables: (Click here to access the FV and PV tables to use with this problem.) Nancy and Jeff want to start a trust fund for their newborn son, Mark. They have decided to invest $5,000 today. If interest is 8% compounded semiannually, how much will be in the fund when Mark turns 20? Round your answer to the nearest dollar. $ Nixon Corporation wants to establish a retirement fund. Management wants to have $1,000,000 in the fund at the end of 40 years. If fund assets will earn 12%, compounded annually, how much will need to be invested now? Round your answer to the nearest dollar. $ How many payments would Star, Inc., need to make if it purchases a new building for $100,000 with annual payments made at the end of each year of $16,401.24 and interest of 16%, compounded annually? Round your answer to the nearest whole value. payments An investment broker indicates that an investment of $10,000 in a CD for 10 years at the current interest rate will accumulate to $21,589. What is the current annual rate of interest if interest is compounded annually? Round to the nearest whole percentage value. %

Solution

Solution 1:

Investment amount = $5,000

Interest rate = 8%, 4% semi annual

Period of investment = 20 years or 40 semiannual period

Future value of fund = P (1+r)^t = $5,000 (1+ 0.04) ^40

= $5,000 * 4.801021 = $24,005

Solution 2:

Future value of fund = $1,000,000

Interest on fund assets = 12%

Period of investment = 40 years

Let amount to be invested is P

Now

P * (1+r)^t = $1,000,000

P ( 1 + 0.12) ^40 = $1,000,000

P = $1,000,000 / 93,05097 = $10,747

Hence amount to be invested today is $10,747

Solution 3:

Purchase value of building = $100,000

Annual installment = $16,401.24

Interest rate = 16%

Let number of payments to be made to settle loan = n

Now

Annual installment = $100,000 / Cumulative PV factor at 16% for n period

Cumulative PV factor at 16% for n period = $100,000 / $16401.24 = 6.097099

On review of PV table, cumulative PV Factor at 16% falls at n = 25

Therefore 25 installment should be paid in order to settle the loan.

Solution 4:

Investment amount (P) = $10,000

Future value = $21,589

Period (n) = 10 years

Let interest rate = i

Now

P (1+i) ^n = $21,589

$10,000 (1+i)^10 = $21,589

(1+i)^10 = 2.1589

1+i = (2.1589) ^ 1/10

1+i = 1.08

i = 8%