Question

1. Answer the following questions:

A) On April 30, 2020, Connie borrowed P 185,000 at 10% compounded monthly. The loan is to be paid out in 90 equal monthly payments with the first payment on May 31, 2020. What is the size of each monthly payment?

B) Cocoy wants to accumulate P 230,000 in 9.5 years. Equal deposits are made at the end of each quarter in an account that pays 15% compounded quarterly. What is the size of each deposit?

C) A man deposits P 5,200 at the end of each three months in an account paying 14% converted quarterly. In order to accumulate P105,000, how many regular deposits every quarter must he make, and what is the size of the concluding deposit, if one is needed?

Answer 1

Solution A
	PV of annuity for making pthly payment
	P = PMT x (((1-(1 + r) ^- n)) / i)
	Where:
	P = the present value of an annuity stream	185000
	PMT = the dollar amount of each annuity payment	P
	r = the effective interest rate (also known as the discount rate)	10.47%	(1+10%/12)^12)-1)
	i=nominal Interest rate	10.00%
	n = the number of periods in which payments will be made	7.5	90/12
	PV of annuity=	PMT x (((1-(1 + r) ^- n)) / i)
	185000=	PMT x (((1-(1 + 10.47%) ^- 7.5)) / 10%)
	Annual payment=	185000/ (((1-(1 + 10.47%) ^- 7.5)) / 10%)
	Annual payment=	35,160.20
	Monthly payment=	2,930.02
Solution B
	FV of annuity
	P = PMT x ((((1 + r) ^ n) - 1) / i)
	Where:
	P = the future value of an annuity stream	230000
	PMT = the dollar amount of each annuity payment	To be computed
	r = the effective interest rate (also known as the discount rate)	15.87%	(1+15%/4)^4)-1)
	i=nominal Interest rate	15.00%
	n = the number of periods in which payments will be made	9.5
	Future value of annuity=	PMT x ((((1 + r) ^ n) - 1) / i)
	230000=	PMT x ((((1 + 15.87%) ^ 9.5) - 1) / 15%)
	Annual deposit=	230000/((((1 + 15.87%) ^ 9.5) - 1) / 15%)
	Annual deposit=	11,308.26
	Quarterly deposit=	2,827.07
Solution C
	FV of annuity
	P = PMT x ((((1 + r) ^ n) - 1) / i)
	Where:
	P = the future value of an annuity stream	105000
	PMT = the dollar amount of each annuity payment	20800	(5200*4)
	r = the effective interest rate (also known as the discount rate)	14.75%	(1+14%/4)^4)-1)
	i=nominal Interest rate	14.00%
	n = the number of periods in which payments will be made	To be computed
	Future value of annuity=	PMT x ((((1 + r) ^ n) - 1) / i)
	105000=	20800*((((1 + 14.75%) ^ T) - 1) / 14%)
	105000/20800=	(1.1475)^T) - 1) / 14%)
	5.048076923	=(1.1475)^T) - 1) / 14%)
	5.04807692307692*14%	=(1.1475)^T) - 1
	0.706730769	=(1.1475)^T) - 1
	1+0.706730769230769	=1.1475^T
	1.706730769	=1.1475^T
	Log (1.70673076923077)	T* log 1.1475
	0.232165018092333=	T* 0.0597613991717461
	T=	0.232165018092333/0.0597613991717461
	T=	3.88	years
	T=	15.54	Quarters