Question

Katy contributes 6% of her salary tp a pension plan at the end of each year. She strated this year with the salary of $70,000 per year. Assuming that her salary is increased by 3% and the interest rate of the pension plan is 7%. Calculate the amount of money in her account after 10 years.

a.33,266

b.48696

c.55,493

d. 95,787

Answer 1

Future value = [(70,000 x 0.06 x 1.07) + (70,000 x 1.03 x 0.06 x 1.078) + (70,000 x 1.032 x 0.06 x 1.077) + ... + (70,000 x 1.039 x 0.06)

Future value = (70,000 x 0.06)[(1.07%) + (1.03 x 1.078) + (1.032 x 1.07") + ... + (1.039)

Future value = 4, 200x [(1.07%) + (1.03 x 1.078) + (1.032 x 1.074) + ... + (1.039)

Formula for GP will be helpful here, which is:

Sum =ax (4=;)

Here,

a is first term.

r is common difference.

n is number of terms.

In the last step of equation,

a is 1.07^9.

r is (1.03/1.07)

n is 10.

Future value = 4, 200 Ox 14.079) (1 - (1:02) (1.07') x 1 1 - 1.03

Future value = 4,200 x [(1.07°) 8.474963352

Future value = 4, 200 x 15.58087445

Future value = 65, 439.67

The amount of money in account after 10 years is $65,439.67.