Question

An accounting firm agrees to purchase a computer for $190,000 (cash on delivery) and the delivery date is in 270 days. How much do the owners need to deposit in an account paying 0.75% compounded quarterly so that they will have $190,000 in 270 days?

Answer 1

Answer:

$188,947

Explanation:

Data provided in the question:

Future value = $190,000

Time, t = 270 days = \text{ 270 days } =$\frac{ 270 }{365}$ = 0.73973 years

Interest rate = 0.75% = 0.0075

Compounded quarterly i.e number of periods n = 4

Now,

Future value = Amount invested × $( 1 + \frac{r}{n} \right)^{\Large{n \cdot t}}$

or

$190,000 = Amount invested × $( 1 + \frac{0.0075}{4} \right)^{\Large{4\times0.73973 }}$

or

$190,000 = Amount invested × ${ 1.00188 } ^ { 2.95892 }$

or

Amount invested = $188,947