Answer: He would have had more $192.288 if the interest were compounding weekly
Explanation:
Let us solve the problem in 2 steps
Step 1
We would determine the amount compounded semi-annually for 30 years.
Initial amount deposited into the account is $7,500. This means that the principal,P = $7,500
It was compounded semi-annually This means that it was compounded twice in a year. So
n = 2
The rate at which the principal was compounded is 3.6%. So
r = 3.6/100 = 0.036
It was compounded for a total of 30 years.
n = 30
The formula for compound interest is
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of n years.
A = 7500(1 + (0.036/2)^2×30
A = 7500(1 + 0.018)^60
A = 7500(1.018)^60
A= $21873.987
Step 2
We would determine the amount compounded weekly for 30 years.
Initial amount deposited into the account is $7,500. This means that the principal,P = $7,500
It was compounded weekly. This means that it was compounded 52 times in a year. So
n = 52
The rate at which the principal was compounded is 3.6%. So
r = 3.6/100 = 0.036
It was compounded for a total of 30 years.
n = 30
Applying the formula for compound interest,
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of n years.
A = 7500(1 + (0.036/52)^52×30
A = 7500(1 + 0.000692)^1560
A = 7500(1.000692)^1560
A = $22066.275
Difference in amount
= $22066.275 - $21873.987 = $192.288