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)883500P=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≈2.85043500P≈$1226.63P≈$1226.63So, the principal amount was approximately $1226.63.
