Question

1) If ​$4000 is deposited in a savings account that earns interest at an annual rate of 2.5​% interest compounded​ continuously, what is the value of the account at the end of two ​years?

2) A trust fund for a 11​-year-old child is being set up by a single payment so that at age 21 the child will receive ​$37,000. Find how much the payment is if an interest rate of 9​% compounded semiannually is assumed.

3) A bank account pays 5.5​% annual​ interest, compounded monthly. How much must be deposited now so that the account contains exactly ​$12,000 at the end of one year​?

Answer 1

1)	Value of account at the end of 2 years	=	P	*	e^(i*n)		Where,
		=	$   4,000.00	*	2.7183^(0.025*2)		P	=	$         4,000.00
		=	$   4,000.00	*	1.051271		e	=	2.7183	(A mathematical constant)
		=	$   4,205.09				i	=	2.50%
							n	=	2
2)	Present value	=	P	*	(1+i)^-n		Where,
		=	$ 37,000.00	*	(1+0.045)^-20		P	=	$      37,000.00
		=	$ 37,000.00	*	0.414643		i	=	4.50%
		=	$ 15,341.79				n	=	20
3)	Present value	=	P	*	(1+i)^-n		Where,
		=	$ 12,000.00	*	(1+0.0045833)^-12		P	=	$      12,000.00
		=	$ 12,000.00	*	0.946604		i	=	0.0045833
		=	$ 11,359.25				n	=	12