Question

How much money should be deposited today in an account that earns 5% compounded semiannually so that it will accumulate to $8000 in three years? The amount of money that should be deposited is $ (Round up to the nearest cent.) You deposit $14,000 in an account that pays 5% interest compounded quarterly A. Find the future value after one year B. Use the future value formula for simple interest to determine the effective annual yield. A. The future value is $ (Round to the nearest cent as needed.)

Answer 1

1. The formula of accumulated value is

m AV P(1 -)" m.

Here AV is the accumulated value, P is the amount to be invested today, r is the rate of return, m is the number of times money is compounded in per unit of n, n is the number of years

So, we have the following details:

r = 5%

AV = $8000

n = 3 years

Since the money is compounded semi-annually, m = 2

So, we need to find P. If we plug in the numbers in the formula, we'll get

$8000 = P( 1 + (0.05/2))^(3*2)

$8000 = P(1.025)⁶

Using calculator we find the value of 1.025⁶ is 1.160 approx

So, $8000 = P * 1.160

Dividing both sides by 1.160, we get

8000/1.160 = (P * 1.160)/1.160

So, 8000/1.160 = P i.e. P = $6896.55

So, the amount to be deposited is $6896.55