Suppose that you want to earn Php 9,281.25 after 27 months and you have Php 75,000. At what rate should you invest the said amount?

a) 5.25%

b) 5.50%

c) 5.75%

d) 11.50%

 

The present value of an ordinary annuity is used to compute the amount of a single deposit to be made today into an account earning interest of 6 percent per year compounded monthly. The deposit must be sufficient to cover a withdrawal of an equal amount each month for 10 years. At

the end of the 10 years, the balance in the account should be $0. To solve for the amount needed (the present value), the total number of conversion period (n) is __________ and the

interest rate per conversion period is __________.

 

a)10 periods, 6 percent

b)10 periods, 0.5 percent

c)120 periods, 6 percent

d)120 periods, 0.5 percent

 

Answer:

At the end of the 10 years, the balance in the account should be $0. To solve for the amount needed (the present value), the total number of conversion period (n) is 120 and the interest rate per conversion period is 0.5%.

Answer: D. 120 periods, 0.5 percent

Step-by-step explanation

Question #1.

Suppose that you want to earn Php 9,281.25 after 27 months and you have Php 75,000. At what rate should you invest the said amount?

The formula for simple interest earned is:

• I = P*r*t/100

Where:

• I is the interest, I = Php 9281.24
• P is the present value, P = Php 75000
• t is the time in years, t = 27 months x (1 year/12 months) = 2.25 years
• r= ?, is the rate of interest;

So;

• I = P*r*t/100
• 92881.25 = 75000*r*2.25/100
• r = 92881.25*100/(75000*2.25) = 5.5
• r = 5.50%

Interest rate, r = 5.50%

Question #2.

The present value of an ordinary annuity is used to compute the amount of a single deposit to be made today into an account earning interest of 6 percent per year compounded monthly.

*Thus, the interest rate per year, r = 6%. Now, since it compounds monthly, then the interest rate per conversion (which is monthly) is:

• Interest rate per conversion = r/12
• Interest rate per conversion = 6%/12
• Interest rate per conversion = 0.5%

The deposit must be sufficient to cover a withdrawal of an equal amount each month for 10 years.

*So, each deposit is conducted every month for 10 years, thus the total number of conversion period is:

• n = 10 years x 12 months/year
• n = 120, that is, there will be a total for 120 deposits.