Question

Please help with the steps​

Answer 1

Answer:

First problem: monthly payment $2741.99; interest earned $76,288.36

Second problem: amount in account $28,271.90; interest earned $4271.90

Step-by-step explanation:

First problem:

You open an account with a deposit. The deposit is the first monthly payment. This means that this is an annuity in which you pay at the beginning of the pay period. That makes it into an "annuity due."

$A = \dfrac{F}{\frac{(1 + i)^n - 1}{i} \times (1 + i)}$

where A = periodic payment,

F = future value

i = interest rate per compounding period, n = number of compounding periods

$A = \dfrac{175000}{\frac{(1 + \frac{0.058}{2})^{2 \times 18} - 1}{\frac{0.058}{2}} \times (1 + \frac{0.058}{2})}$

$A = 2741.99$

Interest earned:

$2 \times 18 \times 2741.99 - 175000 = 76288.36$

Second problem:

Once again, the account starts with a deposit of the monthly payment, so this is also an annuity due, meaning the payments occur at the beginning of each compounding period. Here, we are given the monthly payment, an d we need to find the future value.

$F = A \times \dfrac{(1 + i)^n - 1}{i} \times (1 + i)}$

$F = 400 \times \dfrac{(1 + \frac{0.063}{12})^{5 \times 12} - 1}{\frac{0.063}{12}} \times (1 + \frac{0.063}{12})}$

$F = 28271.90$

The interest earned is:

$28271.90 - 12 \times 5 \times 400 = 4271.90$

Answer 2

Answer:

2821.51

73425.64

28124.24

4124.24

Step-by-step explanation:

Effective rate: .058/2 = .029

This question is kind of ambigous and I'll make the assumption that there is no payment at time 0

$175000=x\frac{(1+.029)^{2*18}-1}{.029}\\x=2821.511$

interested earned:

175000-2821.51*36= 73425.64

2.)

Same assumption as question 1 (there is no payment at time 0)

effective rate: .063/12= .00525

$400(\frac{(1+.00525)^{60}-1}{.00525})=28124.24$

Interest earned: 28124-400*60=4124.24