Question

you have $5,000 you want to invest for the next 45 years. you are offered an investment plan that will pay you 6 percent per year for the next 15 years and 10 percent per year for the last 30 years. what will be your investment value at the end of year 45?○ $201,516.38● $209,092.54○ $221,408.97question 21 ptyou and your sister are planning a large anniversary party 3 years from today for your parents 50th wedding anniversary. you have estimated that you will need $4,500 for this party. you can earn 2.5 percent compounded annually on your savings. how much would you and your sister have to deposit today in one lump sum to pay for the entire party?○ $4,076.55● $4,178.70○ $4,368.81○ $4,308.16○ $4,334.90

Explanation:

Step1: Calc value after 15 years

Use future value formula: $FV_1 = PV \times (1+r_1)^{t_1}$
$PV = 5000$, $r_1=0.06$, $t_1=15$
$FV_1 = 5000 \times (1+0.06)^{15} = 5000 \times 2.396558193 = 11982.79$

Step2: Calc value after 45 years

Use $FV_1$ as new PV for 30 years: $FV_2 = FV_1 \times (1+r_2)^{t_2}$
$r_2=0.10$, $t_2=30$
$FV_2 = 11982.79 \times (1+0.10)^{30} = 11982.79 \times 17.44940227 = 209092.54$

Step3: Calc present value for Question 2

Use present value formula: $PV = \frac{FV}{(1+r)^t}$
$FV=4500$, $r=0.025$, $t=3$
$PV = \frac{4500}{(1+0.025)^3} = \frac{4500}{1.076890625} = 4178.70$

Answer:

1. $\$209,092.54$
2. $\$4,178.70$