Question

New parents wish to save for their newborn's education and wish to have $35,000 at the end of 16 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 8.2% compounded annually? (Round your answers to two decimal places.)
$  

How much interest would they earn over the life of the account?
$  

Determine the value of the fund after 9 years.
$  

A corporation creates a sinking fund in order to have $530,000 to replace some machinery in 8 years. How much should be placed in this account at the end of each week if the annual interest rate is 6% compounded weekly? (Round your answers to the nearest cent.)
$  

How much interest would they earn over the life of the account?
$  

Determine the value of the fund after 2, 4, and 6 years.

2 years		$
4 years		$
6 years		$

Answer 1

1.(a). Formula for calculating Annuity payment ( future value )

P = ( FV × r ) ÷ { (1+r)ⁿ - 1 }

Here, P = Annuity payment

FV = future value = $35000

r = rate per period = 8.2 ÷ 100 = 0.082

n = number of compounding periods = 16

Putting values in the formula we get

P = ( 35000 × 0.082 ) ÷ { (1+0.082)¹⁶ - 1 } = $1134.89

(b). Total amount deposited = 1134.89 × 16 = $18158.24

Total interest earned = 35000 - 18158.24 = $16841.76

(c). Formula for calculating future value of an annuity

FV = [ P × { (1+r)ⁿ - 1 } ] ÷ r

Here, P = $1134.89

r = 0.082

n = 9

Putting values in the formula we get

FV = [ 1134.89 × { (1+0.082)⁹ - 1 } ] ÷ 0.082 = $14290.88