Answer :

Answer: approximately $1226.63.

Step-by-step explanation:

To calculate the amount of money accumulated after 22 years with quarterly compounding interest at a rate of 5.5%, you can use the formula for compound interest:

A=P×(1+r/n)^nt

Where :

-A is the amount of money accumulated after the interest has been compounded for a certain number of years.

-P is the principal amount (the initial amount of money invested).

-r is the annual interest rate (in decimal form).

-n is the number of times the interest is compounded per year.

-t is the time the money is invested for, in years.

Given:

A = $3500

r=5.5%=0.055 (in decimal form)

n=4 (quarterly compounding)

t==22 years

We need to find the principal amount (P).

First, rearrange the formula to solve for P:

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

​Now, plug in the given values:

P=3500(1+0.055/4)^4×22

P=3500(1+0.01375)88P=(1+0.01375)883500​P=3500(1.01375)88P=(1.01375)883500​

Now, calculate (1.01375)88(1.01375)88:(1.01375)88≈2.8504(1.01375)88≈2.8504P≈35002.8504P≈2.85043500​P≈$1226.63P≈$1226.63So, the principal amount was approximately $1226.63.