5. When he turned 42, Jim started to contribute to his retirement account by making an annual deposit of $2500, which is matched by his employer by 150% in an ordinary annuity bearing 9  % interest compounded semiannually.

How much will he have available for him when he retires at 65?

ER = (1 + NR/m) m - 1

= (1 + 0.095/2)2 - 1 = 9.726%

Future value = A * ((1 +r) n - 1)/r)

= (2500 + 3750) * ((1+0.09726)23 - 1) / 0.09726

= $479,029

If Jim wishes to have a total of $600,000 in his IRA when he retires, How much should his (and his employer's) annual contribution be? Consider the same (r) and (n) of question# 5-a.

Future value = A * ((1+r)n - 1)/r) * (1+r)

600000 = A * ((1+0.09726)23 - 1) / 0.09726 * (1+0.09726)

A = 600000 / 80.7596

A= $7,426.73

Consider question #5-a and suppose that Jim's contribution is $2000 but matched by his employer as double (two for one). Also, suppose that Jim's goal is to accumulate half a million dollars in his IRA. At what age should his retirement be to achieve that goal, given that his account bears 10% interest compounded semiannually?

ER = (1 + NR/m) m - 1

= (1 + 0.10/2)2 - 1 = 10.25%

Future value = A * ((1 +r) n - 1)/r )

500000 = (2000 + 4000) * ((1+0.1025) n - 1) / 0.1025

n = (rounded to higher year) 24 Years

In 24 Years, the annuity required amount is a little short. At Age 66 Jim should be able to achieve his goal z.

PART B-

6.For the following 6-a, 6-b, and 6-c, recalculate what you did in 5-a through 5c assuming that the retirement contributions are deposited in an annuity-due account.

a.

 

b.

 

c.