Question

Please give step by step working using the actuarial method with formulas.

Jane makes payments continuously at a rate of $30,000 per year. The payments are made between year 2 and year 7. Find the accumulated value of these payments at year 11, using an annual effective interest rate of 8%.

Answer 1

Continous annual payment between year 2 and year 7 = $30,000 per year

No of periods of paymnets between year 2 and year 7 = 6

Calculating the Future value of these payments at the end of year 7 using Present Value of Ordinary Annuity formula:-

Where, C= Periodic Payments =$30,000
r = Periodic Interest rate = 8% (Annual effective interest rate)
n= no of periods = 6

Future Value = $220,077.87
Now, from beginning of year 8 to end of year 11 the account will accumulate only interest.

No of periods from beginning of year 8 to end of year 11 =4

Calculating the value at the end of year 11:-

Future Value = Amount*(1+r)^n

FV = $220,077.87*(1+0.08)^4

So, value accumulated at year 11 is $299,413.51