how much would you invest today to have $9500 in 8 years if the effective annual rate of interest is 4%?
suppose that an investment of $5750 accumulates to $11533.20 at the end of 13 years, then the effective annual interest rate is i= ?
at an effective annual rate of interest of 5.3%, the present value of $7425.70 due in t years is $3250. determine t

a) You should invest $6941.90 today.

b) The effective annual interest rate is 11%.

c) t is approximately 6.

Step-by-step explanation:

These are compound interest problems. The compound interest formula is given by:

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

a) How much would you invest today to have $9500 in 8 years if the effective annual rate of interest is 4%?

Here, we want to find the value of P when .

.

You should invest $6941.90 today.

b) Suppose that an investment of $5750 accumulates to $11533.20 at the end of 13 years, then the effective annual interest rate is i= ?

Here, we have that , and we want to find the value of i, that is r on the formula above the solutions.

The effective annual interest rate is 11%.

c) At an effective annual rate of interest of 5.3%, the present value of $7425.70 due in t years is $3250. Determine t.

Here, we have that and we have to find t. So

We have that:

log_{a}a^{n} = n

So

t is approximately 6.

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)