# Annuities and Sinking Funds - Calculating Lump Sum Needed

Carolyn Ellis is setting up an annuity for her retirement. She can set aside $2,000 at the end of each year for the next 20 years and it will earn 6% annual interest. What lump sum will she need to set aside today at 6% annual interest to have the same retirement fund available 20 years from now? How much more will Carolyn need to invest in periodic payments than she will if she makes a lump sum payment if she intends to accumulate the same retirement balance?

© BrainMass Inc. brainmass.com October 9, 2019, 11:40 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/annuities-sinking-funds-calculating-lump-sum-needed-263728

#### Solution Preview

Solution:

First let us compute the future value of annuity of 2,000 at 6% for 20 years

Here R = $2000, i = 0.06, n = 20

FV = R((1+i)^n-1)/i

FV ...

#### Solution Summary

A step by step solution is provided through calculations with small worded explanation. The expert calculates the lump sum for sinking funds.