Question

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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 5^th 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!

Answer 1

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