The general formula is
A = P ( 1 + [tex] \frac{I}{100}) ^ t[/tex]
Where:
P = principal that becomes A in t years at the rate I% compound interest per annum.
Here the rate is 7% per annum (12 months)
So I is 1.75% per quarter (3 months)
So t will also be in quarters.
Put:
A = 45000
I = 1.75
t = 20 (since there are 20 quarters in 5 years)(5 years * 4 quarters per year)
45000 = P* [tex] \frac{1.75}{100} ^{20} [/tex]
P = [tex] \frac{45000} {1.0175^{20} }[/tex]
= [tex] \frac{45000}{1.41477819576} [/tex]
≈$31807.12
Thus, the amount that should be invested is $31,807.12
