Today is your 10th birthday, and you decide to start saving for your college education. You will begin college on your 20th birthday and will need to pay ksh144,000 at beginning of first in a 4- year program. Fees will increase at inflation rate of 10% per year. You will make a deposit 1 year from today in an account paying 12% (percent) annually and continue to make an identical deposit each year up to and including the year you begin college. What should be the size of your deposit?

The size of your deposit should be $13,023.92.

Step-by-step explanation:

First, the real interest has to be calculated using the following formula:

r = [(1 + i) / (1 + inf)] - 1 (1)

Where;

i = market interest rate = Interest rate on the account = 12%, or 0.12

r = real interest rate = ?

inf = inflation rate = 10%, or 0.10

Substituting the values into equation (1) and solve for r, we have:

r = [(1 + 0.12) / (1 + 0.10)] - 1 = 0.0181818181818183

Since you will need to pay ksh144,000 at beginning of first in a 4- year program, this implies that the relevant to use in calculating the size of the deposit is the formula for calculating the Future Value (FV) of an Annuity Due as follows:

FV = P * (((1 + r)^n - 1) / r) * (1 + r) (2)

Where,

FV = Future value or the amount needed to pay on the 20th birthday = ksh144,000

P = Fixed annual payment or size of the deposit = ?

r = real interest rate = 0.0181818181818183

n = number of years = 20 - 10 = 10 (Since you will make a deposit 1 year from today annually and continue to make an identical deposit each year up to and including the year you begin college.)

Substituting the values into equation (2) and solve for P, we have:

144,000 = P * (((1 + 0.0181818181818183)^10 - 1) / 0.0181818181818183) * (1 + 0.0181818181818183)

144,000 = P * 10.8591414092614 * 1.0181818181818183

144,000 = P * 11.0565803439752

P = 144,000 / 11.0565803439752

P = $ 13,023.92

Therefore, the size of your deposit should be $13,023.92.

5

step-by-step explanation:

b, 20 yards

step-by-step explanation: