Question

You have two saving accounts, one with a nominal interest rate of 5% and the other with a nominal interest rate of 7%, and both are compounded twice a year. At the end of 10 years, the total in the two accounts is $1000. At the end of 20 years, the amount in the first account is twice the amount in the second account. What is the total in the two accounts after 5 years?

Answer 1

Amount in first Savings Account = S1
Amount in second Savings Account = S2

S1*(1+7%/2)¹⁰ + S2*(1+5%/2)¹⁰ =1000 (Equation 1)
1.410599 * S1 + 1.280085*S2 =1000

S1*(1+ 7%/2)^20*2 = 2*S2*(1+5%/2)²⁰
3.95696 S1 = 5.370128 S2 (Equation 2)

Solving for S1 we get S1 =226.9627
S2 = 334.6678

Total In 2 accounts after 5 years = 226.9627*(1+7%/2)^10+ 334.6678 *(1+5%/2)^10 = 748.56

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