SHOW YOUR WORK PLEASE, I need to know how to do the formulas. Please type the an

Question

SHOW YOUR WORK PLEASE, I need to know how to do the formulas. Please type the answers, I have a hard time reading some peoples handwritting.

For all problems, “1 year” = 12 months = 52 weeks 360 days

1. Mark makes his first deposit of $1500 into a Roth IRA earning 6.5% interest compounded annually at age 36. He continues to make an annual deposit of $1500 until he is 60 (25 deposits in all). With no additional deposits after age 60, the money in Mark’s Roth IRA continues to earn 6.5% interest compounded annually until he retires at age 66. How much money is in Mark’s Roth IRA when he retires?

2. The Smith’s family takes out a 30-year mortgage at 4.25% compounded monthly after putting 20% down to buy a home valued at $220,000.

Find:    a. the monthly payment

b. the unpaid balance after 10 years

c. the equity the family has built up in its house after 20 years of monthly payments, if the house’s net market value 20 years from now is $300,000

Explanation / Answer

1) Here the principle amount is $1500 annually for 25 Years. That means, every year mark is investing $1500 continuously for 25 Years.

The compouned interest per year is 6.5%. For first year, mark invests $1500 & earns interest of $98 @ 6.5% interest per annum. At the end of first year, his total earnings will be ($1500+$98) $1598.

For Second year, he invests additional $1500 so the interset will be calculated for $1500 + $1598 (balance of year 1) at 6.5%.

This process of calculating interest on previous closing balance plus additional current year invests is known as compounded method of calculating interest.

Below table shows the calculation of total balance at the time of Mark's retiral.$137,266.

Year Investment Opening Balance Interest @ 6.5% Closing Balance 1           1,500        1,500             98        1,598 2           1,500        3,098           201        3,299 3           1,500        4,799           312        5,111 4           1,500        6,611           430        7,040 5           1,500        8,540           555        9,096 6           1,500      10,596           689      11,284 7           1,500      12,784           831      13,615 8           1,500      15,115           982      16,098 9           1,500      17,598        1,144      18,742 10           1,500      20,242        1,316      21,557 11           1,500      23,057        1,499      24,556 12           1,500      26,056        1,694      27,750 13           1,500      29,250        1,901      31,151 14           1,500      32,651        2,122      34,773 15           1,500      36,273        2,358      38,631 16           1,500      40,131        2,609      42,740 17           1,500      44,240        2,876      47,115 18           1,500      48,615        3,160      51,775 19           1,500      53,275        3,463      56,738 20           1,500      58,238        3,785      62,023 21           1,500      63,523        4,129      67,652 22           1,500      69,152        4,495      73,647 23           1,500      75,147        4,885      80,032 24           1,500      81,532        5,300      86,832 25           1,500      88,332        5,742      94,073 26      94,073        6,115    100,188 27    100,188        6,512    106,700 28    106,700        6,936    113,636 29    113,636        7,386    121,022 30    121,022        7,866    128,888 31    128,888        8,378    137,266

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