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Peo deposits M3,500 into an account that pays 3.7% compounded annually for the first 4 years, 4.2% compounded annually for the next 4 years, and 4.8% compounded annually for the final 2 years. How muc

Mathematics

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3 parts
a

M3,901.76\text{M3,901.76}

b

M4,394.02\text{M4,394.02}

c

M5,231.97\text{M5,231.97}

Step-by-step solution

8 steps

Part 3

Initial deposit (PP) = M3,500

Interest rates:

  • First 4 years: r1=3.7%=0.037r_1 = 3.7\% = 0.037
  • Next 4 years (years 5-8): r2=4.2%=0.042r_2 = 4.2\% = 0.042
  • Final 2 years (years 9-10): r3=4.8%=0.048r_3 = 4.8\% = 0.048

Part a

M3,901.76\text{M3,901.76}

after 3 years

  1. Identify the values for the first period.

    P=M3,500P = M3,500
    r1=0.037r_1 = 0.037
    t=3t = 3 years

  2. Use the compound interest formula.

    FV=P(1+r1)tFV = P(1 + r_1)^t

  3. Substitute the values and calculate.

    FV=M3,500(1+0.037)3FV = M3,500(1 + 0.037)^3 FV=M3,500(1.037)3FV = M3,500(1.037)^3 FV=M3,500×1.114789FV = M3,500 \times 1.114789 FV=M3,901.76FV = M3,901.76

    After 3 years, the amount in Peo's account will be M3,901.76\boxed{\text{M3,901.76}}.

Part b

M4,394.02\text{M4,394.02}

after 6 years

  1. Calculate the amount after the first 4 years.

    P1=M3,500P_1 = M3,500
    r1=0.037r_1 = 0.037
    t1=4t_1 = 4 years

    FV1=P1(1+r1)t1FV_1 = P_1(1 + r_1)^{t_1} FV1=M3,500(1+0.037)4FV_1 = M3,500(1 + 0.037)^4 FV1=M3,500(1.037)4FV_1 = M3,500(1.037)^4 FV1=M3,500×1.155919FV_1 = M3,500 \times 1.155919 FV1=M4,045.72FV_1 = M4,045.72

  2. Use FV1FV_1 as the new principal for the next period.

    The next period is for 6−4=26 - 4 = 2 years at r2=0.042r_2 = 0.042.
    P2=M4,045.72P_2 = M4,045.72
    r2=0.042r_2 = 0.042
    t2=2t_2 = 2 years

    FV2=P2(1+r2)t2FV_2 = P_2(1 + r_2)^{t_2} FV2=M4,045.72(1+0.042)2FV_2 = M4,045.72(1 + 0.042)^2 FV2=M4,045.72(1.042)2FV_2 = M4,045.72(1.042)^2 FV2=M4,045.72×1.085764FV_2 = M4,045.72 \times 1.085764 FV2=M4,394.02FV_2 = M4,394.02

    After 6 years, the amount in Peo's account will be M4,394.02\boxed{\text{M4,394.02}}.

Part c

M5,231.97\text{M5,231.97}

after 10 years

  1. Calculate the amount after the first 4 years (from part b).

    FV1=M4,045.72FV_1 = M4,045.72

  2. Calculate the amount after the next 4 years (total 8 years).

    P2=FV1=M4,045.72P_2 = FV_1 = M4,045.72
    r2=0.042r_2 = 0.042
    t2=4t_2 = 4 years

    FV2=P2(1+r2)t2FV_2 = P_2(1 + r_2)^{t_2} FV2=M4,045.72(1+0.042)4FV_2 = M4,045.72(1 + 0.042)^4 FV2=M4,045.72(1.042)4FV_2 = M4,045.72(1.042)^4 FV2=M4,045.72×1.177216FV_2 = M4,045.72 \times 1.177216 FV2=M4,763.45FV_2 = M4,763.45

  3. Calculate the amount after the final 2 years (total 10 years).

    P3=FV2=M4,763.45P_3 = FV_2 = M4,763.45
    r3=0.048r_3 = 0.048
    t3=2t_3 = 2 years

    FV3=P3(1+r3)t3FV_3 = P_3(1 + r_3)^{t_3} FV3=M4,763.45(1+0.048)2FV_3 = M4,763.45(1 + 0.048)^2 FV3=M4,763.45(1.048)2FV_3 = M4,763.45(1.048)^2 FV3=M4,763.45×1.098304FV_3 = M4,763.45 \times 1.098304 FV3=M5,231.97FV_3 = M5,231.97

    After 10 years, the amount in Peo's account will be M5,231.97\boxed{\text{M5,231.97}}.

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