Question

An individual wishes to deposit an amount of money now and $100 every six months so that at the end of five years $1,650 will have been accumulated.   With interest at 4% per year, compounded semiannually, how much should be deposited now?

A. $455.35                                          

B. $510.95                           

C. $332.24                           

D. $284.51

Answer:_________________

Show work

Answer 1

Solution:-

Let the amount deposit now is = X

Therefore 100 deposit at every 6 month

Accumulated amount after 5 year is $1650

Interest rate 4% per year, compounded semi-annually

$1650 = X (1 + 0.04/2) ^ (5*2) + 100{(1 + 0.04/2) ^ (5*2) – 1 / i/2}

$1650 = X (1 + 0.04/2) ^ 10 + 100{(1 + 0.04/2) ^ 10 – 1 / 0.04/2}

$1650 = X (1.2190) + 100{1.2190 – 1 / 0.02}

$1650 = X (1.2190) + 100{10.95}

$1650 = X1.2190 + 1095

$1650 - 1095 = X1.2190

$558 = X1.2190

X = $558 / 1.2190

X = $457.75

So the answer is (A) $455.35