25 POINTS!!!!Gabe is getting married in three years and wants to save $20,000 for his wedding. He opens an account earning 6% interest, compounded monthly. Find the periodic monthly deposit (payment) needed to achieve a balance of $20,000 after three years.
Accepted Solution
A:
Answer: $509Step-by-step explanation:Given : Gabe is getting married in three years and wants to save $20,000 for his wedding. He opens an account earning 6% interest, compounded monthly. According to the given description, we haveA= $20,000 , r= 6%=0.06 , t= 3 years , n= 12 [1 yearn = 12 months]Formula to find Periodic monthly deposit :-[tex]P=\dfrac{A\left(\dfrac{r}{n}\right)}{\left(1+\dfrac{r}{n}\right)^{\left(n\cdot t\right)}-1}[/tex]Substitute given values in the above formula , we get[tex]P=\dfrac{20000\left(\dfrac{0.06}{12}\right)}{\left(1+\dfrac{0.06}{12}\right)^{\left(3\cdot12\right)}-1}\\\\=\dfrac{100}{1.19668052482-1}\\\\=\dfrac{100}{0.19668052482}=508.438749031\approx509[/tex]Hence, the periodic monthly deposit (payment) needed to achieve a balance of $20,000 after three years= $509.