Answer:
The money in the account would have been worth about $225.34 more if it was compounded weekly.
Explanation:
Compound-interest formula:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt), where
- A is the amount in the account,
- P is the principal (i.e., the deposit)
- r is the interest rate (note that the percentage is converted to a decimal when using the formula,
- n is the number of compounding periods per year,
- and t is the time in years.
Step 1: Determine the amount in the account when the money is compounded semi-annually:
Before we can use the formula, we must determine which values can be substituted for the variables and which variable we're solving for:
- We want to know the amount in the account, so we're solving for A.
- The $6500 deposit is P.
- 3.9% as a decimal is 0.039, so it's r.
- Money compounded semi-annually is compounded twice per year so 2 is n.
- Our time is 30 years, so it's t.
(Note that it's better to not round until get we get to the very end of the problem so that we get an exact answer when determining how much more the account would have when the money is compounded weekly as opposed to semi-annually)
Now we can plug in these values into the compound-interest formula to find A, the amount in the account after 30 years:
A = 6500(1 + 0.039/2)^(2 * 30)
A = 6500(1.0195)^(60)
A = 20708.42948
Step 2: Determine the amount in the account when the money is compounded weekly:
As we did for Step 1, we need to determine which values we can substitute for the variables and which variable we're solving for:
- We want to know the amount in the account, so we're solving for A.
- The only variable that changes is A and n, so we can keep 6500 for P and 0.039 for r.
- Money compounded weekly is compounded once a week and since there 52 weeks in a year, 52 is n.
Now we can plug in these values into the compound-interest formula to find A, the amount in the account after 30 years:
A = 6500(1 + 0.039/52)^(52 * 30)
A = 6500(1.00075)^(1560)
A = 20933.77004
Step 3: Determine the difference in the money's worth semi-annual and weekly compounding periods:
To determine how much more money is compounded weekly than semi-annually, we can subtract the semi-annually compounded amount from the weekly compounded amount.
20933.77004 -20708.42948
225.3405511
225.34
Thus, the money in the account would have been worth about $225.34 more if it was compounded weekly.