Question

please use make sure you use delta (force of interest) in this equation. It's something like e^integral from year2 to year5 (2/t+1)

Problem 1.10 You deposit $5,000 in an account that earns 5% interest compounded annually in years 1 and 2, and thereafter a continuous rate δ(t) 2/(t + 1) (t > 0). What is the value of the account after 5 years?

Answer 1

Answer:

1St Two Years Interest Rate 5%

And next 3 Years Interest Rate 5.127%(continuous compounding)

Effective annual interest rate in case of continuous compounding is:

EAR = e^rs -1

rate of interest(rs) = 5%

EAR=5.127%

Where e = 2.718281828

Year	Op. Deposit	Interest rate	Interest	Closing balance of Deposit
(A)	(B)	( C )	D=B*C	E= B+D
1	5000	5%	250.00	5,250.00
2	5250	5%	262.50	5,512.50
3	5,512.50	5.127%	282.63	5,795.13
4	5,795.13	5.127%	297.12	6,092.25
5	6,092.26	5.127%	312.36	6,404.61