A) A personal account earmarked as a retirement supplement contains $346,000. Su

Question

A) A personal account earmarked as a retirement supplement contains $346,000. Suppose $300,000 is used to establish an annuity that earns 8%, compounded quarterly, and pays $6500 at the end of each quarter. How long will it be until the value of the annuity is $0? (Round your answer UP to the nearest quarter.) quarters

B) A couple who borrow $70,000 for 30 years at 6%, compounded monthly, must make monthly payments of $419.69.

(a) Find their unpaid balance after 1 year. (Round your answer to the nearest cent.)
$  

(b) During that first year, how much interest do they pay? (Round your answer to the nearest cent.)

Explanation / Answer

A). The formula for annuity payment is C = r(PV)/[ 1-(1+r)-n] where C is the amount of periodic (quarterly ) payment, r is the rate of interest per period, PV is the present value and n is the number of periods (quarters). Here, PV = $ 300000, r = ( 8/100)*1/4 = 2/100 = 0.02, and C = $6500. Therefore, we have 6500= 300000*0.02/[ 1-(1.02)-n} or, 1 –(1.02)-n = 6000/6500 = 12/13 or, (1.02)-n = 1-12/13 = 1/13 or, (1.02)n = 13. On taking logarithm of both the sides, we get n log 1.02 = log 13 or, n = log 13/log 1.02 = 1.113943352/0.008600171762 = 129.53 = 130 quarters       (approximately, on rounding off to the nearest quarter.

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