Question

What deposit made at the end of each quarter will accumulate to $10000 in four years at 4% compounded quarterly?

Answer 1

To accumulate $10,000 in four years at 4% compounded quarterly, you would need to deposit approximately $776.71 at the end of each quarter.

Step-by-step explanation:

To find the deposit needed to accumulate a specific amount in a certain time period, we can use the formula for compound interest:

A = P(1 + r/n)nt

Where:

1. A is the future value ($10,000)
2. P is the deposit amount we want to find
3. r is the annual interest rate (4% or 0.04)
4. n is the number of times interest is compounded per year (quarterly, so 4)
5. t is the number of years (4)

Plugging in the values, we get:

$10,000 = P(1 + 0.04/4)4*4

Simplifying,

$10,000 = P(1 + 0.01)16

Next, we isolate the deposit amount P by dividing both sides by (1 + 0.01)16:

P = $10,000 / (1 + 0.01)16

Calculating this, we find that the deposit needed at the end of each quarter is approximately $776.71.