Question

William invested $2,300 in an account paying an interest rate of 2⅛% compounded quarterly. Nolan invested $2,300 in an account paying an interest rate of 2¾% compounded monthly. After 20 years, how much more money would Nolan have in his account than William, to the nearest dollar?

Answer 1

Nolan would have approximately $218.43 more in his account than William after 20 years.

Step-by-step explanation:

To find the amount of money that Nolan would have in his account after 20 years, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:
A is the final amount
P is the principal investment
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years

For William's account:
P = $2,300
r = 2⅛% = 0.02125
n = 4 (compounded quarterly)
t = 20 years

Using the formula, A = $2,300(1 + 0.02125/4)^(4*20) = $2,300(1 + 0.0053125)^80 ≈ $4,003.53

For Nolan's account:
P = $2,300
r = 2¾% = 0.0275
n = 12 (compounded monthly)
t = 20 years

Using the formula, A = $2,300(1 + 0.0275/12)^(12*20) = $2,300(1 + 0.0022917)^240 ≈ $4,221.96

Therefore, Nolan would have approximately $4,221.96 - $4,003.53 = $218.43 more in his account than William after 20 years.