13. Mary and Jacob just married. Due to their financial education from their col

Question

13. Mary and Jacob just married. Due to their financial education from their colleges, they already plan to save for their future. Mary plans to save $200 a month, starting today, for twenty years. Jacob plans to save $225 a month for twenty years, starting one month from today. Both Mary and Jacob expect to earn an average return of 9.5 percent on their savings. At the end of the twenty years, Mary will have approximately __________less than Jacob.

14.    Using the information below, you want to know which bank you need to apply your student loan.

          - The First Bank offers personal loans at 7.5 percent compounded quarterly.

          - The Second Bank offers similar loans at 7.25 percent compounded monthly.

          Based on the information above, which one is correct analysis result?

          a.       The First Bank loan has an effective rate of 7.67 percent.

          b.       The First Bank loan has an effective rate of 7.78 percent.

          c.       The Second Bank loan has an effective rate of 7.50 percent.

          d.       The Second Bank loan has an effective rate of 7.67 percent.

          e.       The Second Bank loan has a higher effective rate than the First Bank loan.

Explanation / Answer

Answer 13.

Mary:

Mary save $200 per month for next 20 years
Annual Interest Rate = 9.5%
Monthly Interest Rate = 0.7917%

Accumulated Sum = $200*1.007917^239 + $200*1.007917^238 + $200*1.007917^237 + …. + 200*1.007917 + $200
Accumulated Sum = $200 * (1.007917^240 - 1) / 0.007917
Accumulated Sum = $200 * 711.96010
Accumulated Sum = $142,392.02

Jacob:

Jacob save $225 per month for next 20 years
Annual Interest Rate = 9.5%
Monthly Interest Rate = 0.7917%

Accumulated Sum = $225*1.007917^239 + $225*1.007917^238 + $225*1.007917^237 + …. + 225*1.007917 + $225
Accumulated Sum = $225 * (1.007917^240 - 1) / 0.007917
Accumulated Sum = $225 * 711.96010
Accumulated Sum = $160,191.02

So, Mary will save $17,799 ($160,191.02 - $142,392.02) less than Jacob.

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