What lump sum deposited today at 5% compounded annually for 10 years will provided the same amount as $1,000 deposited at the end of each year for 8 years at 6% compounded annually?
2006-11-04 04:41:12 · 1 answers · asked by Anonymous in Education & Reference ➔ Homework Help
Step 1. Solve the second portion of the problem.
$1000 deposited annually can be written as:
1000 * (1.06^7 + 1.06^6 + 1.06^5 + 1.06^4 ... + 1.06^0), because the deposit is made at the end of the year.
This can also be written as:
yearly deposit * ((1 + interest rate)^(# of years) - 1)/(interest rate) =
1000 * ((1.06)^8 - 1)/.06 = $9897.47
Step 2: Create an equation for the first portion:
x * 1.05^10 = $9897.47
where x is the lump sum deposited today, and 1.05^10 is the interest calculation.
x = 9897.47 / 1.05^10 = $6076.19 (solution!)
2006-11-06 05:19:25 · answer #1 · answered by ³√carthagebrujah 6 · 0⤊ 0⤋