Question

Jimmy deposits $ 3,400 now, $ 2,900 3 years from now, and $ 6,000 6 years from now. Interest is 6 % for the first 3 years and 4 % for the last 3 years.

a. How much money will be in the fund at the end of 6 years?
b. What is the present worth of the fund?
c. What is the uniform series equivalent of the fund (uniform cash flow at end of years 1–6)?

Answer 1

Ans A)

Jimmy deposits $3400 now , $2900 3 years from now amd $6000 6 years from now therefore Future worth of these cash flows that is fund in the deposit at the end of 6 years can be calculated as below

Lets assume I is the investment done at time "t" and we are keen to know the future worth of this investment "I" at time "T" in future with interest rate "r" therefore

FW=I(1+r)^(T-t)

Amount in the fund at the end of 6 years=3400(1.06)^3*(1.04)^3+2900(1.04^3)+6000=$13817.91

Ans B)

If we have Future cash flow "F" at time "T" in near future then PW at time "t" now can be calculated as below

PW=F/(1+r)^(T-t)

Present Worth of the fund=13817.91/(1.06*1.04)^3=$10313.95

Ans C)

Uniform series equivalent of the fund is calculated as below
(EUAW= Equivalent uniform annual worth)

EUAW=PW/(Sum of discounting factor)=10313.95/G

G=(1/(1.06))+(1/1.06^2)+(1/1.06^3)+(1/(1.06^3*1.04))+(1/(1.06^3*1.04^2))+(1/(1.06^3*1.04^3))=5.00303189

EUAW=10313.95/5.00303189

EUAW=$2061.54