Question

12. What is the future worth of P600 deposited at the end of every month for 4 years if the interest rate is 12% compounded quarterly?

Ans P36.641

13. A young woman 22 years old, has just graduated from college. She accepts a good job and desires to establish her own retirement Fund Ar the end of each year thereafter she plans to deposit P2,000 in a fund at 15% annual interest. How old will she be when the fund has an accumulated value of P1.000.000?

 Ans. 53 years old 

14. Mr Reyes borrows P600 000 at 12% compounded annually areng to repay the loan in 15 equal annual payments. How much of the original principal is still unpaid after he has made the 8th payment? 

Ans P 402,040

Answer 1

12. formula to compute the future value of an annuity with periodic payment A for T periods, given periodic return r :

= A ( (1+r)^T- 1)/r

In this question, the monthly deposit is 600 for 4 years. There are in total 48 deposits. The effective monthly interest rate is:

= (1+12%/4)^1/3 - 1 = 0.99%

On applying the formula,

= 600 ( (1+ 0.99%)⁴⁸ -1 )/0.99% = P36,641.32

13. Given, Future value of annuity = P1,000,000.

Each deposit amount = P2,000

Interest rate = 15%

Let the number of years be "n"

Formula for future value is ( as seen in previous answer)= A( (1+r)ⁿ-1)/r

On substitution of these values,

1,000,000 = 2,000( (1+0.15)ⁿ-1)/0.15

On solving , n = 31 years approximately (30.9865)

She will be 22+31 = 53 years old

14. we can find the annuity value using the given information,

Formula for present value of annuity = A ( 1- (1+r)^-n)/n

Where, present value of annuity = P600,000

A = monthly installment

r= rate if interest = 0.12

n = no.of years = 15 years

On substitution, A = 88,094.54

Then get the P where A = 88 094.54, i=0.12 , n=7 because after 8 payments the remaining payments is 7.

Using the same formula,

P = P402,042.05