Answer:
a. $4307.96
b. 4.76 years
c. $0.99
Explanation:
These questions can be answered using the relevant formulas for future value of an investment.
a.
For compound interest, the account balance is given by ...
A = P(1 +r/n)^(nt) . . . . principal P at annual rate r compounded n times per year for t years
$4000 at 2.48% compounded quarterly for 3 years will give an account balance of ...
A = $4000(1 +0.0248/4)^(4·3) = $4000×1.0062^12 ≈ $4307.96
After 3 years, there will be $4307.96 in the account.
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b.
After earning $500 in interest, the account balance will be $4500. That means we need to solve for t such that ...
4500 = 4000(1.0062^(4t))
log(4500/4000)/(4×log(1.0062)) = t ≈ 4.764
It will take about 4.76 years to earn $500 interest.
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c.
The future value of an account with continuous compounding is given by ...
A = Pe^(rt)
A = $4000e^(0.0248·3) ≈ $4308.95
Then the additional interest is ...
$4308.95 -4307.96 = $0.99
If the money is compounded continuously, there will be $0.99 more in the account after 3 years.