Question

An individual saves $5000 in a bank account at the beginning of each year for 10 years.

Answer 1

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: $A=P(1+\frac{r}{n})^{nt}$

Putting values:

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

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: $A=P(1+\frac{r}{n})^{nt}$

Putting values:

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

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