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Linda made a deposit of $400 in her savings account 5 years ago. In the first year her account was earning 6%, but she did not deposit any money. In the second year the interest increased to 8%, when Linda knew about the increase she deposited C amount at the end of year 2. During the third year the interest increased again to 11% which made Linda deposit double the amount that she deposited the year before (2C). In the fourth and the fifth year the interest rate dropped to 7%. By the end of the 5th year she had $3,074.39 in hear account. What is the value of C deposited in the account to make Linda Savings $3,074.39?
Thank you!
Starting deposit=Co=$400
Interest rate in year 1=i1=6%
Interest rate in 2nd year=i2=8%
Future value of Co at the end of 2nd year=Co*(1+i1)*(1+i2)=400*(1+6%)*(1+8%)=$457.92
Principal amount at the beginning of 3rd year=P3=(457.92+C)
Interest rate in 3rd year=i3=11%
Future value of P3 at the end of 3rd year=(457.92+C)*(1+11%)=508.2912+1.11C
Principal amount at the beginning of 4th year=P4=508.2912+1.11C+2C=508.2912+3.11C
Interest rate for 4th and 5th year=i4=7%
Future value of P4 at the end of 5th year=(508.2912+3.11C)*(1+7%)2=581.9426+3.560639C
We are given that
581.9426+3.560639C=3074.39
or C=(3074.39-581.9426)/3.560639=$700
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