A. Refer to Narrative 12-1. Angie needs to have an annuity payment of $1,300, at

Question

A. Refer to Narrative 12-1. Angie needs to have an annuity payment of $1,300, at the BEGINNING of each year for 10 years. How much should she deposit now at 10% interest, compounded annually, to yield this payment?

B. Refer to Narrative 12 - 1. Alicia deposited $1,300, at the BEGINNING of each year for 9 years in an account at her credit union. If the account paid 11% interest, compounded annually, find the future value of her account.

C. Refer to Narrative 12-1.Jan purchased a new tool set costing $899.99 by taking out a 7.25% add - on installment interest from her credit union. She is paying the loan in equal payments over one year. How much are Jan's monthly payme nts? (Round to the nearest cent)

Explanation / Answer

A.

Here, payment is done in the beginning of each year. Thus, it is a case of annuity due.

Now, we have to calculate the present value of all payments in 10 year time @ 10% interest rate.

R = 10%

n = 10 years

Present value of payment = 1300*((1-1/(1+R)^n)/R)*(1+R)

Present value of payment = 1300*((1-1/1.1^10)/.1)*1.1 = $8786.74

Thus, Angie should deposit $8786.74 to get the annuity payment of $1300 at the beginning of each year for 10 years

B.

Here, payment is done in the beginning of each year. Thus, it is a case of annuity due.

P = $1300

R = 11%

n = 9 years

Future value of all payments = P*((1+R)^n – 1)/R)*(1+R)

Future value of all payments = 1300*((1.11^9 - 1)/.11)*1.11 = $20438.61

Thus, Alicia will get $20438.61 in her account as a future value.

C.

Cost of the tool = $899.99

Annual interest rate = 7.25%

Thus, monthly interest rate (R) = 7.25%/12 = .6042%

n= 12 months

Let , monthly payment = EMI

Now,

899.99 = EMI*(1-1/(1+R)^n)/R = EMI*(1-1/1.006042^12)/.006042

899.99 = EMI*11.5417

EMI = $77.98

Thus, Jan’s monthly payment is $77.98.

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