Question

1. In order to save for her high school graduation, Kathrina decided to save ₱200 at the end of every other month, starting the end of the second month. If the bank pays 0.250% compounded monthly, how much will be her money at the end of 5 years? (use j = 0.000417, n = 30)
2. Emma availed of a cash loan that gave her an option to pay ₱10,000 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% converted monthly?

Answer 1

Answer:

1) 202.52

2) P107089

Step-by-step explanation:

Compound interest is calculated as

A = P (1 + r/n)^(nt), where

A = compounded interest

P = present value

r = interest

n = number of times interest applied

t = time taken

A = 200 (1 + 0.25%/30)^(30 * 5)

A = 200 (1 + 8.3*10^-5)^150

A = 200 * 1.0126

A = 202.52

Present Value Annuity Due is usually given by the formula

P = c*((1-(1+ i)^(-n))/i)*(1 + i ), where

P is the present value

C is the Cash flow per period

i is the interest rate and

n is the number of payments

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

P = 113676

Also, it's worthy of note that

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

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

EAR = 12.68%

And lastly, the

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

113676 = Present value*(1+0.1268)^0.5

Present Value = 113676 / 1.1268^0.5

Present Value = 113676 / 1.0615

Present value = 107089