What is the lump sum?

Question

Find the lump sum deposited today that will yield the same total amount as payments of $14,000 at the end of each year for 13 years, at an interest rate of 6% compounded annually

Answer 1

 

Because there are annual payments, the regular compound interest formula will not work.

 

The formula is:

 

P(1 + r)^t + c[ ((1 + r)^t + 1 - (1 + r)) / r ] found at http://www.moneychimp.com/articles/finworks/fmbasinv.htm

 

Where P is the starting principal, c is the regular deposit or payment, r is the interest rate, and t is the time

 

In this problem, P=c = $14,000,   r = 6% = 0.06, and t = 13

 

1 +r = 1 +6% = 100% + 6% = 106% = 1.06

 

14000(1.06)^13 + 14000 [ ((1.06)^13 + 1 - 1.06))/.06 ]