a, Calculate the future sum of $3.000, given that it will be held in the bank fo
ID: 2813943 • Letter: A
Question
a, Calculate the future sum of $3.000, given that it will be held in the bank for 7 years at an APR of 5 percent. b. Recalculate part (a) using compounding periods that are (1) semiannual and (2) bimonthly (every two months) c. Recalculate parts (a) and (b) for an APR of 10 percent. d. Recalculate part (a) using a time horizon of 14 years (the APR is stil 5 percent) e. With respect to the effect of changes in the stated interest rate and holding periods on future sums in parts (c) and (d), what conclusions do you draw when you compare these figures with the answers found in parts (a) and (b)? a. What is the future sum of $3,000 in a bank account for 7 years at an APR of 5 percent? (Round to the nearest cent)Explanation / Answer
a)
Future Value = Present Value * (1+rate of period)^no. of period
= 3000*1.05^7
= 3000*1.4071
= 4221.30
b)
Future Value = Present Value * (1+(rate per year/no. of compounding per year))^(no. of period*no. of compounding per year)
1)Semi annual compounding
Future Value = 3000 * (1+(.05/2))^(7*2)
= 3000 * 1.025^14
= 3000*1.4129
= 4238.92
1)Bimonthly compounding
Future Value = 3000 * (1+(.05/6))^(7*6)
= 3000 * 1.0083^42
= 3000 * 1.415043
= 4245.13
c)
Future Value = Present Value * (1+rate of period)^no. of period
= 3000*1.1^7
= 3000*1.9487
= 5846.10
1)Semi annual compounding
Future Value = 3000 * (1+(.1/2))^(7*2)
= 3000 * 1.05^14
= 3000*1.97993
=5939.79
1)Bimonthly compounding
Future Value = 3000 * (1+(.1/6))^(7*6)
= 3000 * 1.0167^42
= 3000 * 2.0049
= 6014.70
d)
Future Value = Present Value * (1+rate of period)^no. of period
= 3000*1.05^14
= 3000*1.97993
= 5939.79
e) When the interest rate increases from 5% to 7% there is also an increase in future value.Also we can see an increasing trend in future value when compunding per year increases.When the holding period increases from 7 years to 14 years, then also the future value increases.Since
Future Value = Present Value * (1+rate of period)^no. of period
In general we can say that there is a direct relationship between future value and interest rate and holding period
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