Answer:
John must invest $3719.4
Explanation:
It is given that John grandfather withdraws $120 per month for 3 year
So total month = 12 ×3 =36 months
Total amount withdrawn S = 36×120 = 4320
m = 12 times per year
Rate of interest i = 5 % = 0.05
We know that [tex]S=P(1+\frac{i}{m})^{mt}[/tex]
[tex]4320=P(1+\frac{0.05}{12})^{36}[/tex]
[tex]4320=P\times 1.1614[/tex]
P = $3719.41
So john must invest $3719.4
The total amount of money that the john should invest is as a principal is $3,719.41.
Compound interest is the amount of interest that is paid or received on the accumulated amount of money,
Means firstly is paid or received on the principal, then it is calculated on the amount of principal with the amount of previous interest.
Computation of amount of principal:
According to the given condition,
Interest rate(r)= 5%
Fraction when compounded monthly for three years:
[tex]r=\dfrac{\frac{5}{12} }{100} \\\\r=0.0041[/tex]
Number of period(n)is 3 years means:
[tex]3\text{Years}\times\text{12 Months }= 36 \text{Months}[/tex]
Then total amount withdrawn per year is $120 for 3 years is:
[tex]3\text{Months}\times\$120 =\$4,230[/tex]
Now apply the formula of compound amount to get the invested amount is:
[tex]A=\text{P}(1+i)^n}[/tex]
Now substitute the given values in the formula:
[tex]A=\text{P}(1+i)^n}\\\\\$4,320=\text{P}(1+0.0041)^3^6}\\\\\$4,320= P(1.1614)\\\\\text{P}= \$3,719.41[/tex]
Therefore, the invested amount at the starting of the year is $3,719.41.
Learn more about compound interest, refer to:
https://brainly.com/question/25857212
