Answer:
a) present value $33,872.11
b) future value $44, 399.43
Explanation:
The question is asking for two values
1. The present value of Rich Aunt Frederica's planned $10,000 per yer for 4 years
2. The future value of the plan if the gift of $10,000 is invested at 7% per annum in 4 years.
First, to calculate the present value, the formula is to use the 7% rate to discount the annual value of $10,000 as follows:
Formula for discounting = P / (1+r)∧n
P= Payment
r= yearly rate
n= number of years.
Year 1 10,000/ (1.07)∧1 $9,345.79
Year 2 10,000/ (1.07)∧2 $8,734.39
Year 3 10,000/(1.07)∧3 $8162.98
Year 4 10,000/ (1.07)∧4 $7628.95
Total $33,872.11
Secondly, to calculate the future value , formula is to multiply the annual value by the 7% annual rate raised to the period.
Formula for discounting = P x (1+r)∧n
P= Payment
r= yearly rate
n= number of years.
Year 1 10,000 x (1.07)∧1 $12,250.43
Year 2 10,000 x (1.07)∧2 $11,449
Year 3 10,000 x (1.07)∧3 $10,700
Year 4 10,000 x (1.07)∧4 $10,000
Total $44, 399.43
