Question

1. Jill starts working on her 28th birthday with an annual salary of $57,000 that is expected to rise by 2.5% cach year. She sets aside 6.5% of her annual salary at the end of each year for her pension plan, whsh is matched by her employer (i.e., a total of 13% of her salary, that is $7,410 will be deposited in the pension plan at the end of the year and this amount will increase by 2.5% cach subsequent year). She hopes her retirement account can make 4.5% per year interest average. Caluclate the amount in her pension plan on her 65th birthday

Answer 1

The first step is to calculate the present value of the deposits for a period of 38 years starting from 28th birthday and ending on 65th birthday.

The present value of deposits is found using the present value of growing annuity equation

(0) 2015

PV = $7410 x (1 + 0.025 387 0.045 -0.025 0.045 -0.025 (1 +0.045

Present value of the deposits = $ 192,722.8

The future amount in the pension plan is found using future value of investment equation

Future value = Present value $\times$ ( 1 + interest )ⁿ

Amount in the pension plan on her 65th birthday = $ 192,722.8 $\times$ ( 1 + 0.045)³⁸

Amount in the pension plan on her 65th birthday = $ 1,026,483.9 $\approx$ $ 1,026,484