Question

1. Assume you are planning to invest $200 each year for four years and will earn 8 percent per year. Determine the future value of this annuity due problem if your first $200 is invested now.

Answer 1

Answer:

The future value of the $200 invested yearly for 4 years at 8% is $973.32

Explanation:

The future value of an immediate annuity is given by the formula = (1+r)*[P*((1+r)^n-1)/r]

P=is the periodic payment of $200

r=rate of return=8 percent

n=number of years=4

By slotting the variables into the formula we have:

Fv=(1+0.08)*(200*((1+0.08)^4-1)/0.08)

FV=$973.32

Judging by the concept of time value of money, it is expected that the sum invested at interest would have been much more at maturity of the investment as $1 today should give a lot more than $1 in future.

Answer 2

Answer:

$242.10

Explanation:$P= C (1+(R/N)) ^T$

P= Future Value  

C= Amount invested/ present value =$200

R= interest rate of invested amount = 8%

N= periods invested per year = 1

T= the number of years the amount is invested times by the number of periods invested per year. = 4years

Substitute the above values to the formulae $P=C(1+(R/N))^T$

Then you get :$P=200(1+0.08)^4$ thereafter you compute this on a calculator as value n=1 and T= 4*1= 4, then you get the below value of $242.097792 which is rounded off to the bottom answer of

P=$242.10

for the problem you solve for P given the other values which you substitute on the formula given above as it is mentioned that the interest is awarded annually. The number of periods n is 1 because it is annually compounded and the investment earns interest on interest because there is no withdrawal being don over the years in between being invested.

By using this formula you are showing that after a year if you invest $200 with an interest rate of 8% it will be $216 then this amount plus interest for year 1. $216 will be reinvested to earn an interest of 8% for the second year which the end vale will be $233.28. For the third year again the second years amount with its interest will be reinvested for 8% interest for the third year therefore calculated as $233.28*1.08= $251.94. then for the last 4th year we invest the third years amount at an interest rate of 8% which will be calculated as $251.9424*1.08=  $272.097792 then we round off to two decimal places for the final answer $272.10. That is how we got to the final answer.