Question

DEFERRED ANNUITY 

Instruction: Solve the given situations. Show your solutions 

1. Emma availed of a cash loan that gave her an option to pay P10,000 monthly for 1 year. The first payment is due after 6 months. How much is the present value of the loan if the interest rate is 12% compounded monthly?

 2. Adrian purchased a laptop through the credit cooperative of their company. The cooperative provides an option for a deferred payment. Adrian decided to pay after 4 months of purchase. His monthly payment is computed as P3,500 payable in 12 months. How much is the cash value of the laptop if the interest rate is 8% compounded monthly?

 3. Mr. and Mrs. Mercado decided to sell their house and to deposit the fund in a bank. After computing the interest, they found out that they may withdraw P350,000 yearly for 4 years starting at the end of 7 years when their child will be in college How much is the fund deposited if the interest rate is 3% compounded annually?

Answer 1

1

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 10000*((1-(1+ 12/1200)^(-1*12))/(12/1200))*(1+12/1200)

PV = 113676.28

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

? = ((1+12/(12*100))^12-1)*100

Effective Annual Rate% = 12.6825

Future value = present value*(1+ rate)^time

113676.28 = Present value*(1+0.126825)^0.5

Present value = 107088.2

Please ask remaining parts seperately, questions are unrelated