Question

Consider the following deposits made into a savings account that earns a constant interest compounded annually. 'An' represents the actual deposits made at the end of year n. 'Pn' represents the present value of the deposit in year n. The present value 'Pn' of $750 in year 2 is $667.40. Assuming there are only 4 deposits made, calculate the total amount in the savings account at the end of year 4. 'An' in $ (Years 0 through 4): 0 440 750 170 0"

Answer 1

We are given that  'An' = actual deposits made at the end of year n. 'Pn' = present value of the deposit in year n.

'Pn'($750, n = 2) = $667.40.

This implies that 750(P/F, i%, 2) = 667.50

750/(1 + i%)^2 = 667.50

This gives i% = (750/667.50)^(1/2) - 1 or i% = 6%.

Now that interest rate is 6%, there are only 4 deposits made, 0 440 750 170 0

Find the accumulated amount at the end of 4 years

F = 440(1+6%)^1 + 750(1 + 6%)^2 + 170(1 + 6%)^3

= $1151.57

This is the total amount in the savings account at the end of year 4.