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An individual saves $5000 in a bank account at the beginning of each year for 10 years.
No further savings or withdrawals are made from the account. Determine the total amount saved if the annual interest rate is 8% compounded:
(a) annually;
(b) semi-annually.

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Answer:

a) Amount saved if the interest is compounded annually is $5832

b) Amount saved if the interest is compounded semi-annually is $5849.5

Step-by-step explanation:

Principal Amount P = 5000

Time t = 10 years

Annual interest i = 8% = 0.08

We need to find amount saved if interest is compounded a) annually b) semi-annually

a) Amount saved if the interest is compounded annually

If interest compounded annually, n= 1

Using Formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Putting values:

[tex]A=P(1+\frac{r}{n})^{nt} \\A=5000(1+\frac{0.08}{1})^{1*2}\\A=5000(1+0.08)^2\\A=5000(1.08)^2\\A=5000(1.1664)\\A=5832[/tex]

So, Amount saved if the interest is compounded annually is $5832

b) Amount saved if the interest is compounded semi-annually

If interest compounded semi-annually, n= 2

Using Formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Putting values:

[tex]A=P(1+\frac{r}{n})^{nt} \\A=5000(1+\frac{0.08}{2})^{2*2}\\A=5000(1+0.04)^4\\A=5000(1.04)^4\\A=5000(1.1699)\\A=5849.5[/tex]

So, Amount saved if the interest is compounded semi-annually is $5849.5

(a). When compounded annually, the amount will be [tex]\$ 10,794.6[/tex]

(b). When compounded semi-annually, the amount will be [tex]\$ 10,955.6[/tex]

Compound interest:

It is given that, an individual saves $5000 in a bank account at the beginning of each year for 10 years.

[tex]Principal(P)=5,000, t=10 years, rate(r)=8\%[/tex]

As we know that,

               [tex]Amount=P(1+\frac{r}{100} )^{t} \\\\Amount=5,000(1+\frac{8}{100})^{10} \\\\Amount=5,000*(\frac{108}{100})^{10}\\\\Amount=\$ 10,794.6[/tex]

When interest is compounded semi-annually;

[tex]r=8/2=4\%, t=10*2=20[/tex]

             [tex]Amount=5,000(1+\frac{4}{100})^{20} \\\\Amount=5,000*(\frac{104}{100})^{20}\\\\Amount=\$ 10,955.6[/tex]

Learn more about the compound interest here:

https://brainly.com/question/24924853