Which would amount to more money on December 31 of this year: $500 invested on January 1st of this year at 10% annual interest compounded quarterly; or a lump sum payment of $580?
(a) the $500 investment (b) both are the same
(c) the $580 lump sum (d) there is not enough information to determine
500*(1 + .025)^4 = 551.91
The lump sum ($580) is more.
To determine which option would amount to more money on December 31 of this year, we need to calculate the future value of the $500 investment and compare it to the $580 lump sum payment.
To calculate the future value of the investment, we can use the formula for compound interest:
Future Value = P(1 + r/n)^(nt)
Where:
P is the principal amount (initial investment)
r is the annual interest rate (10% in this case)
n is the number of times interest is compounded per year (quarterly in this case)
t is the number of years (from January 1 to December 31 of the same year)
For the $500 investment, we can calculate the future value as follows:
Future Value = $500(1 + 0.10/4)^(4 * 1)
Calculating this, we get:
Future Value = $500(1.025)^4
Future Value ≈ $500(1.108155)
Future Value ≈ $554.08
So, the future value of the $500 investment on December 31 of this year is approximately $554.08.
Comparing this to the $580 lump sum payment, we can conclude that (c) the $580 lump sum would amount to more money on December 31 of this year.