Question

You are a financial adviser working with a client who wants to retire in eight years. The client has a savings account with a local bank that pays 8% annual interest. The client wants to deposit an amount that will provide her with $1,003,500 when she retires. Currently, she has $301,400 in the account. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.)

How much additional money should she deposit now to provide her with $1,003,500 when she retires? (Round your answer to nearest whole dollar.)

Answer 1

x = $240759.82559797761 rounded off to $240.759.83

Step-by-step explanation:

To calculate the additional amount that is required to be invested today, we will use the formula for Future value of a cash flow.

FV = PV * (1+r)^t

Where,

• FV and PV are future value and present value respectively
• r is the interest rate or rate of return
• t is the time period

We know the Future value that is the sum required and we know the r which is 8% and t which is 8 years. We know the partial PV which is 301400 and we need to calculate the other part of PV. Thus we can say that PV = 301400 + x

Solving the equation for x where x is the additional money that should be deposited today.

1003500 = (301400 + x) * (1+0.08)^8

1003500 / (1+0.08)^8 = (301400 + x)

542159.8255977329 = 301400 + x

542159.8255977329 - 301400 = x

x = $240759.82559797761 rounded off to $240.759.83