Question

Assume that you want an investment of $1,000 today to yield $1,216.65 in five years and want to know the nominal interest rate for the investment.

a) Use the RATE function in Excel to calculate your answer.

b) Now use the tables and guidance from the text to calculate the nominal interest rate.

Answer 1

a)

Pmt = As there is no periodic payment it will be 0.

PV is cash outflow. Since it is an initial investment that will be paid. It results into outflow. Hence 'minus' is used.

FV is cash inflow . Since it is the value to be received after 5 years. It results into inflow. Hence 'plus' used.

The reference used in solving the RATE function is seen in the formula bar.

Please give a look at the formula bar in the image below.

New_Microsoft_Excel_Worksheet - Saved v Ą O 5 co fx =RATE( B1 ,0,- B2 ,+ B3 ) A B 1 5 2 Period (Years) Initial Investment(Outflow)(PV) Future value (Inflow) 1000 3 1216.65 4 4% 5 Nominal Interest rate. 6 Rate(Nper,Pmt,PV,FV,type,guess) 7 Nper= Period 8 Pmt = Payment 9 PV = Present value 10 FV = Future value 11 Remaining arguments are optional. 12 13 14 15 16 17 18 19 20 21 22 23 24 to .00 →.0 ая a .00

b) Using the formula

Amount = Principal ( 1 + r)^t

Where r is rate & t is time.

Formula for rate can be derieved as follows :

(Amount / Principal) = ( 1 + r)^t

(Amount / Principal)^ (1/t) = 1 + r

(Amount / Principal)^ (1/t) - 1 = r   

where (1/t) = (1/5)= 0.2

Rate= (Amount / Principal)^ (1/t) - 1

= (1216.65/1000)^0.2 - 1

= (1.21665)^0.2 - 1

= 1.04 - 1 = 0.04 or 4 %