Consider the following deposits made into a savings account

\"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 $770 in year 2 is $703.20. 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): 0 540 770 290 0\"

Solution

Present value of $770 in year 2 = 703.2

It means that,

703.2 = 770/(1+R)^2

Here, R = interest rate

(1+R)^2 = 770/703.2 = 1.094994

R = 1.094994^(1/2) -1

R = 4.642%

Now,

Future value of all deposits at the end of year 4 = 540*1.04642^3 + 770*1.04642^2 + 290*1.04642

Future value of all deposits at the end of year 4 = $1765.35