The amount that should deposit monthly is $164.98
The formula for calculating the compound amount is expressed as:
![A=P(1+\frac{r}{n} )^{nt}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bnt%7D)
- A is the amount after 18 years = $75000
- r is the rate = 7.5% = 0.075
- t is the time in years = 18 years
- n is the compounding time = 12 (monthly)
Substitute the given values into the formula to have:
![75000=P(1+\frac{0.075}{12} )^{12(18)}\\75000 = P(1.00625)^{216}\\75000 =P(3.84125)\\P = \frac{75000}{3.84125}\\P= \$19,524.89](https://tex.z-dn.net/?f=75000%3DP%281%2B%5Cfrac%7B0.075%7D%7B12%7D%20%29%5E%7B12%2818%29%7D%5C%5C75000%20%3D%20P%281.00625%29%5E%7B216%7D%5C%5C75000%20%3DP%283.84125%29%5C%5CP%20%3D%20%5Cfrac%7B75000%7D%7B3.84125%7D%5C%5CP%3D%20%5C%2419%2C524.89)
Hence the amount of money they started with is $19,524.89.
Amount to deposit monthly = 19,524.89/120
Amount to deposit monthly = $164.98
Hence the amount that should deposit monthly is $164.98
Learn more on compound interest here: brainly.com/question/24274034