Question

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?
Question 47 options:

$5,178.09


$5,436.99


$5,708.84


$5,994.28


$6,294.00

Answer 1

Answer:

$5,178.09

Explanation:

Data provided in the question:

Principle amount, P = $5,000

Interest rate, r = 5.25%

Duration, t = 8 months = $\frac{8}{12}$ years = 0.67 years

Now,

A = $P \left( 1 + \frac{r}{n} \right)^{\Large{n \cdot t}}$

Here,

A = total amount

P = principal or amount of money deposited,

n = number of times compounded per year  i.e 365 for daily

t = time in years

Thus,

A = $5,000 × $\left( 1 + \frac{5.25%}{365} \right)^{\Large{365 \cdot 0.667}}$

=  $5,000 × $( 1.0001437 )^{243.45}$

= $5,000 × 1.035618

= $5,178.09

Hence,

the correct answer is option $5,178.09