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

$188,947

Step-by-step explanation:

Data provided in the question:

Future value = $190,000

Time, t = 270 days = \text{ 270 days } =
`( 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 + (r)/(n) \right)^{\Large{n \cdot t}} $$`

or

$190,000 = Amount invested ×
`( 1 + (0.0075)/(4) \right)^{\Large{4*0.73973 }} $$`

or

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

or

Amount invested = $188,947