Calculate the rate of interest compounded annually if a An i

Calculate the rate of interest compounded annually if:

(a) An investment of $8,000 today accumulates to $20,750 in 10 years.

(b) A series of 5 year-end payments of $5,000 results in an accumulated amount of $30,525.

Let the interest rate be R.

PV = FV x (1 + R)^N

(a)

$20,750 = $8,000 x (1 + R)¹⁰

(1 + R)¹⁰ = $20,750 / $8,000 = 2.5938

Taking 10th root on each side,

1 + R = 1.1

R = 1.1 - 1 = 0.10, or 10%

(b)

FV = Annuity x FVIFA (R%, N)

$30,525 = $5,000 x FVIFA (R%, 5)

FVIFA (R%, 5) = $30,525 / $5,000 = 6.1050

From FVIFA table for 5 years, the value is closes to 6.1050 when R = 10%