You would like to have $3,000 in 4 years for a special vacation following gradua

Question

You would like to have $3,000 in 4 years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays 3.5% compounded semiannually. Determine how much you should deposit at the end of every six months. How much of the $3,000 comes from deposits and how much comes from interest? a. In order to have $3,000 in 4 years, you should deposit $ at the end of every six months. (Do not round until the final answer. Then round up to the next dollar.) b. $ of the $3,000 comes from your deposits and $ comes from interest. (Use the answer from part a to find this answer. Round to the nearest dollar as needed.)

Explanation / Answer

Amount to be deposited at the end of every six months to earn $3,000.

Interest rate =3.5%

Compounded semi annually. Therefore semi annual interst rate =1.75%

Let 1 be the amount invested every six months.

Amount at the end of 4 years is $3,000.

Therefore, amount to be deposited every six months to earn $3,000 =$3,000/8.656412

=$346.56

Answer for point b:

Interest amount in $3,000 is maturity amount minus 8* principal amounts

=$3,000 - $2,772.48

=$227.52.

Instalment Instalment amount Principal interest Principal+interest 1 1 0.0175 1.0175 2 1 2.0175 0.035306 2.052806 3 1 3.052806 0.053424 3.10623 4 1 4.10623 0.071859 4.178089 5 1 5.178089 0.090617 5.268706 6 1 6.268706 0.109702 6.378408 7 1 7.378408 0.129122 7.50753 8 1 8.50753 0.148882 8.656412

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