Question

Periodic Deposit: $? at the end of each monthRate: 7.5% compounded monthlyTime: 3 yearsFinancial Goal: $35,000O A. $2,628; $31,536 from deposits and $3,464 from interestB. $776; $27,936 from deposits and $7,064 from interestO c. $933; $33,588 from deposits and $1,412 from interestOD. $870; $31,320 from deposits and $3,680 from interest

Answer 1

D. $870; $31,320 from deposits and $3,680 from interest

Explanation:

In order to calculate the monthly payment, we use the formula below:

`P=(A\mleft((r)/(n)\mright))/(\mleft[\mleft(1+(r)/(n)\mright)^(nt)-1\mright])`

Given:

• The Financial Goal, A= $35,000

,

• Rate = 7.5% = 0.075

,

• Number of compounding period = 12 (Monthly)

,

• Time, t = 3 years

Substitute into the given formula:

`\begin{gathered} P=(35000\mleft((0.075)/(12)\mright))/(\mleft[\mleft(1+(0.075)/(12)\mright)^(12*3)-1\mright]) \\ P\approx\$870 \end{gathered}`

The monthly payment is $870.

`\begin{gathered} \text{Total deposit}=870*36=31,320 \\ \text{Interests}=35,000-31,320=3680 \end{gathered}`

Option D is correct.