Question

$5,000 is deposited today into a bank account. The account earns 7.5% per annum compounded half yearly for the first 6 years, then 7.8% per annum compounded quarterly thereafter. Assuming no further deposits or withdrawals are made,

(a) Calculate the account balance six months from today.

Answer 1

Answer:

The account balance six months from today is $5,187.5.

Step-by-step explanation:

This is a compound interest problem

The compound interest formula is given by:

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

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that

The total amount formula changes after 6 years, at which point each of the principal(initial money), interest rate, and n changes.

This item asks only the balance six months from today, so we use the information given for the first 6 years.

A is the account balance, the value we hope to find.

The loan is of $5,000. So $P = 5,000$

The account earns 7.5% per annum compounded half yearly, so $r = 0.075, n = 2$.

We want to find the account balance in 6 months. However, t is measured in years. So $t = \frac{6}{12} = 0.5$

Solving the equation:

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

$A = 5,000(1 + \frac{0.075}{2})^{1}$

$A = 5,187.5$

The account balance six months from today is $5,187.5.