Answer:
The amount that should be in its savings account is $40,554.48.
Explanation:
To calculate this, formula for calculating the present value of an ordinary annuity is employed as follows:
PV = P * [{1 - [1 / (1 + r)]^n} / r] …………………………………. (1)
Where;
PV = Present value of or amount in the saving =?
P = yearly scholarship payment = $5,000
r = interest rate = 4%, 0.04
n = number of years = 10
Substitute the values into equation (1) to have:
PV = $5,000 * [{1 - [1 / (1 + 0.04)]^10} / 0.04]
PV = $5,000 * [{1 - [1 / 1.04]^10} / 0.04]
PV = $5,000 * [{1 - 0.961538461538461^10} / 0.04]
PV = $5,000 * [{1 - 0.675564168825795} / 0.04]
PV = $5,000 * [0.324435831174205 / 0.04]
PV = $5,000 * 8.11089577935512
PV = $40,554.48
Therefore, the amount that should be in its savings account is $40,554.48.
